Geochimica et Cosmochimica Acta, Vol. 64, No. 2, pp. 339 –366, 2000
Copyright © 2000 Elsevier Science Ltd
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0016-7037/00 $20.00 ⫹ .00
Pergamon
PII S0016-7037(99)00284-7
Condensation in dust-enriched systems
DENTON S. EBEL1 and LAWRENCE GROSSMAN*,1,2
1
Department of the Geophysical Sciences, The University of Chicago, 5734 South Ellis Avenue, Chicago, IL 60637, USA
2
Enrico Fermi Institute, The University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA
(Received January 11, 1999; accepted in revised form July 9, 1999)
Abstract—Full equilibrium calculations of the sequence of condensation of the elements from cosmic gases
made by total vaporization of dust-enriched systems were performed in order to investigate the oxidation state
of the resulting condensates. The computations included 23 elements and 374 gas species, and were done over
a range of P tot from 10⫺3 to 10⫺6 bar and for enrichments up to 1000⫻ in dust of Cl composition relative to
a system of solar composition. Because liquids are stable condensates in dust-enriched systems, the MELTS
nonideal solution model for silicate liquids (Ghiorso and Sack, 1995) was incorporated into the computer code.
Condensation at 10⫺3 bar and dust enrichments of 100⫻, 500⫻, and 1000⫻ occur at oxygen fugacities of
IW-3.1, IW-1.7, and IW-1.2, respectively, and, at the temperature of cessation of direct condensation of
olivine from the vapor, yields X Fa of 0.019, 0.088, and 0.164, respectively. Silicate liquid is a stable
condensate at dust enrichments ⬎⬃12.5⫻ at 10⫺3 bar and ⬎⬃425⫻ at 10⫺6 bar. At 500⫻, the liquid field
is ⬎1000 K wide and accounts for a maximum of 48% of the silicon at 10⫺3 bar, and is 240 K wide and
accounts for 25% of the silicon at 10⫺6 bar. At the temperature of disappearance of liquid, X Fa of coexisting
olivine is 0.025, 0.14, and 0.31 at 100⫻, 500⫻, and 1000⫻, respectively, almost independent of P tot. At
1000⫻, the Na2O and K2O contents of the last liquid reach 10.1 and 1.3 wt.%, respectively, at 10⫺3 bar but
are both negligible at 10⫺6 bar. At 10⫺3 bar, iron sulfide liquids are stable condensates at dust enrichments
at least as low as 500⫻ and coexist with silicate liquid at 1000⫻. No sulfide liquid is found at 10⫺6 bar. At
10⫺3 bar, the predicted distribution of Fe between metal, silicate and sulfide at 1310 K and a dust enrichment
of 560⫻ matches that found in H-group chondrites, and at 1330 K and 675⫻ matches that of L-group
chondrites prior to metal loss.
Only at combinations of high P tot and high dust enrichment do the bulk chemical composition trends of
condensates reach the FeO contents typical of type IIA chondrules at temperatures where dust and gas could
be expected to equilibrate, ⱖ1200 K. Even under these conditions, however, the composition trajectories of
predicted condensates pass through compositions with much more CaO ⫹ Al2O3 relative to MgO ⫹ SiO2 than
those of most type IA chondrules. Furthermore, on a plot of wt.% Na2O vs. wt.% FeO, most chondrule
compositions are too Na2O-rich to lie along trends predicted for the bulk chemical compositions of the
condensates at P tot ⱕ 10⫺3 bar and dust enrichments ⱕ1000⫻. Together, these chemical differences indicate
that individual chondrules formed neither by quenching samples of the liquid ⫹ solid condensates that existed
at various temperatures nor by quenching secondary liquids that formed from such samples. With the
exception of very FeO-poor, Na2O-rich glasses in type I chondrules and glasses with very high FeO and Na2O
in type II chondrules, however, many chondrule glass compositions fall along bulk composition trajectories
for liquids in equilibrium with cosmic gases at 10⫺3 bar and dust enrichments between 600⫻ and 1000⫻. If
these chondrules formed by secondary melting of mixtures of condensates that formed at different temperatures, nebular regions with characteristics such as these would have been necessary to prevent loss of Na2O
by evaporation and FeO by reduction from the liquid precursors of their glasses, assuming that the liquids were
hot for a long enough time to have equilibrated with the gas. Copyright © 2000 Elsevier Science Ltd
metal reacts with gaseous H2O to form FeO (Grossman, 1972)
which must then diffuse into the crystal structure of previously
condensed forsterite, replacing MgO. At these low temperatures, however, this mechanism for producing the observed
FeO content of olivine in chondrites encounters two fundamental problems: solid– gas equilibrium is unlikely, and diffusion
in olivine is very slow. Enhancing the oxygen fugacity of the
system in which chondritic matter formed is one way FeO
could have been stabilized at temperatures high enough that it
was incorporated into ferromagnesian silicates when, or soon
after, they first condensed.
The most reasonable mechanism proposed for producing the
oxygen fugacity required to form fayalitic olivine at higher
temperatures is enhancement of the dust/gas ratio (Wood, 1967;
Rubin et al., 1988). In such a model, the initial nebula is a cold
cloud of interstellar gas and dust, whose overall composition is
1. INTRODUCTION
Several lines of evidence suggest that most chondrites
formed at oxygen fugacities significantly higher than those of a
solar gas (e.g., Fegley and Palme, 1985; Rubin et al., 1988;
Palme and Fegley, 1990; Weinbruch et al., 1990). The most
compelling evidence is the high FeO content of chondritic
olivine and pyroxene grains, many of which have molar FeO/
(FeO ⫹ MgO) ratios greater than 0.15 (Wood, 1967; Van
Schmus, 1969). Grossman (1972) showed that the first olivine
and pyroxene to condense from a cooling solar gas contain only
trace amounts of FeO, because iron is more stable as cocondensing metallic nickel–iron. At equilibrium, olivine will
not incorporate significant FeO until below 550 K, when iron
*Address reprint requests to Lawrence Grossman.
339
340
D. S. Ebel and L. Grossman
solar and in which ⬃30% of the oxygen is in the dust, and
virtually all of the H and C are in the gas. If, before nebular
temperatures reach their maximum, dust concentrates in certain
regions relative to the gas compared to solar composition, then
total vaporization of such regions will produce a gas enriched
in oxygen relative to hydrogen and carbon compared to solar
composition. Subsequent condensation in such a region occurs
in a gas with a significantly higher oxygen fugacity than one of
solar composition. Furthermore, the abundance ratios of condensable elements such as Mg and Si to H are increased much
more than the O/H ratio, because the dust contains nearly 100%
of each of the condensable elements, compared to only 30% of
the oxygen. The condensation temperature of any phase increases with increasing partial pressures of its gaseous constituents, which in turn increase with their abundances relative to
hydrogen. Dust enrichment therefore not only increases oxygen
fugacity, but also increases condensation temperatures, possibly to temperatures at which partial melts are stable.
Wood and Hashimoto (1993) and Yoneda and Grossman
(1995) performed full equilibrium calculations of condensation
in dust-enriched systems, and both studies found stability fields
of silicate liquids at relatively low total pressure. Therefore, an
accurate thermodynamic description of silicate liquids is a
prerequisite for an accurate description of condensation in
dust-enriched systems. Yoneda and Grossman (1995) were the
first to assess the stability of nonideal CaO–MgO–Al2O3–SiO2
(CMAS) silicate liquid (Berman, 1983), but were unable to
address the stability of ferromagnesian liquids due to lack of an
accurate thermodynamic model for silicate liquids containing
Fe, Ti, Na, and K.
The present work is the first to explore condensation in either
solar composition or dust-enriched systems using a thermodynamic model for ferromagnesian liquids which has been tested
against experimental data and natural assemblages. An 11component subset of the 15-component “MELTS” silicate liquid model, developed by Ghiorso and Sack (1995) to model
crystallization of natural silicate liquids of peridotite to intermediate compositions, has been incorporated into condensation
calculations. In addition, this liquid model is shown here to
describe accurately the crystallization of liquids in the FeO–
CMAS system, similar to many of the liquids predicted in this
work. Condensation sequences are computed at dust enrichments of up to 1000⫻, and at P tot of 10⫺3 and 10⫺6 bar, at
temperatures from 1100 to 2400 K. Results indicate the composition changes in solid, liquid, and gas phases likely to occur
during direct condensation, partial evaporation, or preaccretion
metasomatism of matter in dust-enriched systems at these temperatures and pressures. The idea that ferromagnesian chondrules formed by direct condensation in the solar nebula has
persisted since Sorby (1877) likened chondrules to solidified
“drops of fiery rain”, and Wood (1967) revived it by suggesting
that liquids of forsterite composition might be stable at low
total pressures in gases enriched (by ⬎5000⫻) in precondensed
dust. Therefore, in this work, specific equilibrium assemblages
are compared with specific chondrules, and the implications of
dust enrichment for chondrule stability in the protoplanetary
nebula are explored. Preliminary versions of this work were
presented by Ebel and Grossman (1996, 1997a, 1997b, 1998).
2. TECHNIQUE
2.1. Bulk Composition
The nature of the condensates from dust-enriched bulk compositions
is strongly influenced by the composition assumed for the dust, and an
infinite variety of fractionated dust compositions can be imagined. One
constraint on dust composition, however, is that it led to condensate
assemblages containing chondritic proportions of condensable elements. Cl chondrites are representative of the bulk composition of the
condensable fraction of solar system matter. If the bulk of the condensable elements was originally brought to the solar nebula in the form of
interstellar dust, then it is reasonable to assume that the aggregate
composition of that dust had a bulk chemical composition similar to
that of Cl chondrites. Table 1 shows the relative atomic abundances of
the 23 elements considered in this work in solar gas (Anders and
Grevesse, 1989), the Cl chondrite dust component of solar gas, and
several dust-enriched systems. For a dust enrichment of n, one way to
calculate the bulk composition is by adding (n ⫺ 1) units of the Cl dust
to solar composition. Enrichment factors of up to 1000 were investigated. Although there are as yet no astronomical observations that
confirm, or astrophysical models that produce such enrichments, there
exists no evidence to rule out such enrichments in protoplanetary
environments.
2.2. Method of Calculation
The condensation code described here, “VAPORS”, is described
more completely by Ebel et al. (1999). All calculations are normalized
to a total of one mole of atoms in the system. A typical condensation
run at fixed P tot and bulk composition is begun with only the vapor
phase present at 2400 K. Most solutions are obtained at 10 K intervals,
using the result at the previous temperature as a first approximation. At
each fixed pressure, temperature, and bulk composition of the system,
the partial pressures of the pure monatomic gaseous elements (the basis
components of the gas phase) are obtained by calculating the distribution of the elements among 374 species in the gas phase, using standard
techniques (Lattimer et al., 1978; Smith and Missen, 1982). The stability of each potential, stoichiometrically pure, single component
condensate phase is then evaluated from the partial pressures of the
elements and the Gibbs energy for that phase, by considering the
energy balance of the formation reaction of the condensate from the
monatomic gaseous elements. In the case of a liquid or solid solution
phase, the “best” composition is determined by finding that composition at which the activities of the components describing the solution
phase most closely match equivalent activities in the gas, using the
algorithms of Ghiorso (1994). This composition is then tested for
stability in much the same way as a stoichiometrically pure condensate,
but also accounting for the thermodynamic mixing properties of the
components in the solution phase. In some cases where silicate liquid
is present, this algorithm failed to find the “best” pyroxene solid
solution composition, and the program proceeded with a pure diopside
end-member composition instead. In such cases, the program was
restarted with a “seed”, Ti-, Al-bearing diopsidic pyroxene substituted
for the pure diopside at and above the temperature step at which pure
diopside had been found to be stable. In all such cases, a complex, Ti-,
Al-bearing diopsidic pyroxene was found to be stable at the temperature where pure diopside had been found, or, at most, 20 K higher. The
Gibbs energy of the system was always on the order of 0.5 J lower per
mole of elements in the system for the assemblage with the pyroxene
solid solution than for the one with pure diopside. This problem occurs
only with the pyroxene solid solution model, probably because of the
difficulty in determining both the composition and ordering state of the
near end-member pyroxene in equilibrium with a gas phase highly
depleted in some of the pyroxene-forming elements. Once a phase is
determined to be stable, it is added to the stable assemblage in a seed
amount (10⫺7 mol), which is subtracted from the gas. The next step is
to distribute mass between the phases to minimize the total free energy
of this new system.
In this work, the second order technique of Ghiorso (1985), following Betts (1980), was adapted to the problem of distributing mass
between phases to minimize directly the total Gibbs free energy of a
system consisting of gas and multiple pure and solution phases, both
Condensation in dust-enriched systems
341
Table 1. Relative atomic abundances in solar composition and the Cl component of solar composition, both normalized to 106 atoms Si, and
compositions of systems enriched in dust of Cl composition relative to solar.
Solar
H
He
C
N
O
F
Ne
Na
Mg
Al
Si
P
S
Cl
Ar
K
Ca
Ti
Cr
Mn
Fe
Co
Ni
Cl dust
2.79 ⫻ 10
2.72 ⫻ 109
1.01 ⫻ 107
3.13 ⫻ 106
2.38 ⫻ 107
8.43 ⫻ 102
3.44 ⫻ 106
5.74 ⫻ 104
1.07 ⫻ 106
8.49 ⫻ 104
1.00 ⫻ 106
1.04 ⫻ 104
5.15 ⫻ 105
5.24 ⫻ 103
1.01 ⫻ 105
3.77 ⫻ 103
6.11 ⫻ 104
2.40 ⫻ 103
1.35 ⫻ 104
9.55 ⫻ 103
9.00 ⫻ 105
2.25 ⫻ 103
4.93 ⫻ 104
10
5.28 ⫻ 10
6
7.56 ⫻ 105
5.98 ⫻ 104
7.63 ⫻ 106
8.43 ⫻ 102
5.74 ⫻ 104
1.07 ⫻ 106
8.49 ⫻ 104
1.00 ⫻ 106
1.04 ⫻ 104
5.15 ⫻ 105
5.24 ⫻ 103
3.77 ⫻ 103
6.11 ⫻ 104
2.40 ⫻ 103
1.35 ⫻ 104
9.55 ⫻ 103
9.00 ⫻ 105
2.25 ⫻ 103
4.93 ⫻ 104
solid and liquid. The Gibbs energy of the entire system can be imagined
as a surface in m dimensions, where m is the total number of components independently variable in each of the phases present. The components of the gas are the monatomic elements, while those of solution
phases are the end-members of these phases. Each distribution of
elements between these components at fixed temperature and pressure
defines a state of the system, and corresponds to a point on the Gibbs
surface. In successive iterations, information about the local slope and
curvature of the Gibbs surface at the current state of the system is used
to determine the direction toward a minimum on this surface, along
which the next iterative solution must lie. Then atoms are redistributed
accordingly among the gas and condensates, that is among the m
components, so that this minimum is approached as closely as possible.
From the perspective of this new state of the system, the Gibbs surface
“looks” different, so a new minimum must be sought in a further
iteration. Convergence is declared when the vector norm of all the
changes in composition in the m directions does not change by ⬎10⫺12
between iterations. The VAPORS program usually converges in less
than 10 iterations in this part of the algorithm.
Upon convergence to a free energy minimum, the stabilities of
noncondensed phases are assessed as described above, and if additional
phases are found to be stable relative to the gas, they are added as
described above and the minimization algorithm is repeated. Even trace
phases such as perovskite are typically present at levels ⬎10⫺6 mol per
mole of elements in the complete system. If the amount of a phase
drops below a minimum value, set at 10⫺10 mol, that phase is removed
from the condensate assemblage, and the minimization algorithm is
repeated. If no phase must be added or removed after the minimization,
the system is considered solved for that temperature, pressure, and bulk
composition, and a new temperature step is initiated.
Convergence of each solution is assessed independently by calculation of the difference in the chemical potential of each condensed
component between the gas and condensates. For temperatures ⬎1400
K, these differences for each component are always ⬍10⫺7 of the
chemical potential in the gas, and usually very much better (e.g.,
⬃10⫺12). At lower temperatures, particularly in dust-enriched systems,
these differences in some cases increase for components containing the
elements Ca, Al, and Ti, and no results are reported here for any
temperature step in which the difference exceeds 10⫺4 for any condensate component. Even in an example where these differences are ⬃3 ⫻
10⫺4, they would record uncertainties corresponding to a shift of only
⬃10⫺10 of the total Ca in the system between the gas and the conden-
100 ⫻ Cl
500 ⫻ Cl
1000 ⫻ Cl
2.84 ⫻ 10
2.72 ⫻ 109
8.50 ⫻ 107
9.05 ⫻ 106
7.80 ⫻ 108
8.43 ⫻ 104
3.44 ⫻ 106
5.74 ⫻ 106
1.07 ⫻ 108
8.49 ⫻ 106
1.00 ⫻ 108
1.04 ⫻ 106
5.15 ⫻ 107
5.24 ⫻ 105
1.01 ⫻ 105
3.77 ⫻ 105
6.11 ⫻ 106
2.40 ⫻ 105
1.35 ⫻ 106
9.55 ⫻ 105
9.00 ⫻ 107
2.25 ⫻ 105
4.93 ⫻ 106
3.05 ⫻ 10
2.72 ⫻ 109
3.87 ⫻ 108
3.30 ⫻ 107
3.83 ⫻ 109
4.22 ⫻ 105
3.44 ⫻ 106
2.87 ⫻ 107
5.37 ⫻ 108
4.25 ⫻ 107
5.00 ⫻ 108
5.20 ⫻ 106
2.58 ⫻ 108
2.62 ⫻ 106
1.01 ⫻ 105
1.89 ⫻ 106
3.06 ⫻ 107
1.20 ⫻ 106
6.75 ⫻ 106
4.78 ⫻ 106
4.50 ⫻ 108
1.13 ⫻ 106
2.47 ⫻ 107
3.32 ⫻ 1010
2.72 ⫻ 109
7.65 ⫻ 108
6.28 ⫻ 107
7.65 ⫻ 109
8.43 ⫻ 105
3.44 ⫻ 106
5.74 ⫻ 107
1.07 ⫻ 109
8.49 ⫻ 107
1.00 ⫻ 109
1.04 ⫻ 107
5.15 ⫻ 108
5.24 ⫻ 106
1.01 ⫻ 105
3.77 ⫻ 106
6.11 ⫻ 107
2.40 ⫻ 106
1.35 ⫻ 107
9.55 ⫻ 106
9.00 ⫻ 108
2.25 ⫻ 106
4.93 ⫻ 107
10
10
sate assemblage. These reaction imbalances occur because the algorithms call for numerical approximation of the first and second derivatives of the Gibbs energy of the gas with respect to the concentration
of each of the condensing elements in it, and this approximation
becomes increasingly sensitive to machine numerical precision at very
low concentrations of elements in the gas (e.g., 10⫺20 mol per mole of
elements in the system). Mass balance is preserved to within ⬍10⫺27
of the moles of atoms present throughout all calculations.
2.3. Thermodynamic Data for Elements and Gas Species
In each calculation, 23 elements were included: H, He, C, N, O, F,
Ne, Na, Mg, Al, Si, P, S, Cl, Ar, K, Ca, Ti, Cr, Mn, Fe, Co, and Ni. The
gas species considered in every calculation include all species considered by Grossman (1972) and Yoneda and Grossman (1995), as well as
those listed in Table 2. The ⌬ f H⬚ (298.15 K), S⬚ (298.15 K), and C p ⬚
(T) data for gas species and elements in their standard states were taken
wherever possible from the JANAF tables (Chase et al., 1985), obtained in machine readable form from the National Institute of Standards and Technology in 1995. For a few gas species not present in the
JANAF database, data from Knacke et al. (1991) or Pedley and Marshall (1983) were used. During calculation, apparent Gibbs energies of
formation (Anderson and Crerar, 1993), and hence the equilibrium
constants of reactions, were calculated by integration of polynomial fits
to tabulated C p ⬚ (T) data. Errors were found in the JANAF tabulations
(Chase et al., 1985) of the Gibbs energy of formation (⌬ f G⬚) and
equilibrium constant (ln Kf ) for the gas species C2N2, C2H2, CN, and
HS. The error in HS was also present in the electronic version, and had
not been previously reported (M. Chase, personal communication;
1996). Although it does not occur in the tabulations of Stull and
Prophet (1970), Barin (1989), or Knacke et al. (1991), the HS( g) error
has been propagated through the work of Yoneda and Grossman
(1995), and probably also Sharp and Wasserburg (1995) and others.
The effect of this error is to overestimate the stability of HS( g) , and
cause SiS( g) to sequester slightly less Si than it should.
2.4. Thermodynamic Data and Models for Solids
The internally consistent thermodynamic database of Berman
(1988), or a combination of the internally consistent databases of
342
D. S. Ebel and L. Grossman
Table 2. Gas species and thermodynamic data sources, included in the calculation, in addition to species used by Grossman (1972) and/or Yoneda
and Grossman (1995).
Chase et al. (1985)
Ne
Ar
AlClF
AlClF2
AlCl2
AlCl2F
AlCl3
AlF2
AlF2O
AlF3
NaAlF4
AlHO
Al2
Al2Cl6
Al2F6
CCl
CClFO
CClF3
CClN
CClO
CCl2
CCl2F2
CCl2O
CCl3
CCl3F
CCl4
CF
CFN
CFO
CF2
CF2O
CF3
CF4
CF4O
CF8S
CHCl
ClNO2
ClHO
ClNO
CHClF2
CHCl2F
CHCl3
CHF
CHFO
CHF3
CH2ClF
CH2Cl2
CH2F2
CH3Cl
CH3F
KCN
CN2*
CP
C2Cl2
C2Cl4
C2Cl6
C2F2
C2F4
C2F6
C2HCl
C2HF
C2H4
(KCN)2
Ni(CO)4
Fe(CO)5
CaCl
CaS
CoCl
ClF
ClFO2S
ClFO3
ClF2OP
ClF3
ClF5
ClF5S
FeCl
PCl5
Fe2Cl6
NiCl
ClO
TiOCl
ClO2
PCl
ClS
ClS2
SiCl
TiCl
Cl2
CoCl2
Cl2FOP
FeCl2
SiCl2H2
K2Cl2
SiCl3
NiCl2
Cl2O
TiCl2O
Cl2O2S
Cl2S
Cl2S2
SiCl2
TiCl2
CoCl3
SiCl3F
FeCl3
SiCl3H
POCl3
PCl3
PCl3S
TiCl3
Co2Cl4
Fe2Cl4
Mg2Cl4
SiCl4
TiCl4
SiCl3
NF3
Other sources
CoF2
CrN
CrO
CrO2
CrO3
F10S2
FeF
FHO
FHO3S
SiFH3
SiF3H
FNO
FNO2
FNO3
FO
Na2Cl2
FO2
FPS
SF
SiF
F2
FeF2
H2F2
K2F2
F2N
F2N2*
Na2F2
F2O
SiF2O
TiF2O
SF2O2
PF2
SF2
S2F2*
SiF2
FeF3
SiF2H2
H3F3
H7F7
F3NO
PF3O
PF3
F3PS
SF3
SiF3
TiF3
H4F4
Mg2F4
N2F4
SF4
SiF4
TiF4
TiFO
PF5
H5F5
H6F6
SF6
FeS
NiS
K2O2H2
KO
K2
K2SO4
Na2SO4
HNO2*
P4O10
P4O6
P4
P4S3
S3
S4
S5
S6
S7
Knacke et al. (1991)
CrCl2O2
MnCl2
CrS
MnF2
NiF2
Ni(OH)2
NiO
NiAl2Cl8
NiF
NiH
TiS
CrCl2
Pedley and Marshall (1983)
CoO
MnO
* Both cis and trans forms are included.
Berman and Brown (1985) and Berman (1983) were used wherever
possible for all potential condensates in Table 3 and for most endmember components of the solid solution series in Table 4, except for
the metal alloy. This means that Berman (1988) was the source of
end-member data for the melilite and feldspar solid solutions, not the
references cited for the solution models for these phases. The JANAF
data (Chase et al., 1985) for pyrrhotite, Fe0.877S, are based on estimation of heat capacities from 600 to 1475 K. Recent work below 1000 K
by Grønvold and Stølen (1992) indicates that these data cause overstabilization of pyrrhotite by ⬃5 kJ at 1000 K. Therefore, Gibbs energies
of formation of pyrrhotite from the JANAF tables were revised upward
by this amount in the calculation. This revision lowers the appearance
temperature of pyrrhotite by ⬃50 K, compared to the JANAF data.
The solid solution models implemented in the MELTS program
(circa 1993; Table 4) were used in all calculations, except that Capyroxenes (Sack and Ghiorso, 1994a; 1994b; 1994c) were constrained
to have one total atom of Ca ⫹ Na per six oxygen atoms. These
represent the most comprehensive treatments of the anhydrous igneous
rock-forming minerals presently available, and are the solid solution
models against which the MELTS silicate liquid model is calibrated. In
addition, solid Fe–Ni–Si–Cr–Co alloy was modeled using JANAF data
(Chase et al., 1985) for pure metal end-members, and an asymmetric
binary solution model calibrated against activity data for the binary
systems of Chuang et al. (1986b) for Fe–Ni, Sakao and Elliott (1975)
for Fe–Si, and Normanton et al. (1976) for Fe–Cr, with Fe–Co treated
as ideal. Such a calibration is justifiable for the dilute alloys found at
high temperature in this work.
Some cations of great interest in condensation are not contained in
some of the liquid or solid solution models used here. These are the first
condensation calculations in which the TiO2 content of spinel is modeled, and extraordinarily high TiO2 contents are predicted at very high
temperatures. In all such cases, however, spinel coexists with a CMAS
liquid into which TiO2 is artificially prevented from dissolving. Partitioning experiments (Connolly and Burnett, 1999) suggest that these
high TiO2 contents may be spurious. Insufficient experimental work
exists to justify inclusion of Ti3⫹ or Cr3⫹ in the pyroxene model. No
solution model is used for Mn, S, P, or C in the metal alloy, and this
could artificially enhance the stabilities of troilite, pyrrhotite, and
whitlockite. Similarly, our inability to account for Ni or Co in troilite
or pyrrhotite, nor for Cr, Ti, or Al in olivine, may artificially destabilize
these phases slightly. Although Hirschmann (1991) has modeled Ni,
Co, and Mn in olivine, these elements are not addressed by the
pyroxene model, nor are Ni and Co included in the spinel model
employed here. Because inclusion of Ni, Co, or Mn in only one of these
phases would artificially stabilize that phase and cause it to contain
excessive amounts of these cations, these cations were not included
in the olivine model. This omission, however, artificially stabilizes
MnTiO3-rich rhombohedral oxide solid solutions and crystalline
MnO.
Condensation in dust-enriched systems
343
Table 3. Pure solid phases considered in the calculation, and sources of thermodynamic data.
Miscellaneous solid phasesa
Aenigmatite
Andalusite
Anhydrite
Anthophyllite
Apatite
Brucite
Ca-aluminate
Calcite
Cohenite
Cordierite
Corundum
Cristobalite
Dolomite
Grossite
Hatrurite
Hibonite
Kalsilite
Leucite
Lime
Magnesite
Manganosite
Merwinite
Nepheline
Periclase
Perovskite
Pyrrhotite
Quartz
Rankinite
Rutile
Sapphirine
Sillimanite
Sinoite
Sphene
Talc
Tialite
Tri-Ca aluminate
Tridymite
Troilite
Whitlockite
Wollastonite
Na2Fe5TiSi6O20
Al2SiO5
CaSO4
Mg7Si8O22(OH)2
Ca5(PO4)3OH
Mg(OH)2
CaAl2O4
CaCO3
Fe3C
Mg2Al4Si5O18
Al2O3
SiO2
CaMg(CO3)2
CaAl4O7
Ca3SiO5
CaAl12O19
KAlSiO4
KAlSi2O6
CaO
MgCO3
MnO
Ca3MgSi2O8
NaAlSiO4
MgO
CaTiO3
Fe0.877S
SiO2
Ca3Si2O7
TiO2
Mg4Al10Si2O23
Al2SiO5
Si2N2O
CaTiSiO5
Mg3Si4O10(OH)2
Al2TiO5
Ca3Al2O6
SiO2
FeS
Ca3(PO4)2
CaSiO3
Chase et al. (1985)
M
B8
R
B8
M
B8
B5
B8
R
B8
B8
M
B8
B5
B5
B3
M
M
B8
B8
R
B8
M
B8
R
J
M
B5
B8
B3
B8
F
B8
B8
R
B5
M
C
M
B8
Al
Al4C3
AlN
Al2S3
Al6Si2O13
alpha Ca
beta Ca
CaCl2
CaF2
Ca(OH)2
CaS
CoO
Cr3C2
CrN
Cr2N
Cr2O3
FeCl2
FeF2
Fe0.947O
FeO
Fe(OH)2
Fe(OH)3
FeS2 (Pyrite)
FeSO4
Fe2(SO4)3
Graphite
K
KCl
KF
KF2H
KH
K2O
KOH
K2S
K2SO4
K2SiO3
Mg
MgC2
Mg2C3
MgCl2
MgH2
MgF2
Mg3N2
MgS
Mg2Si
MgSO4
MgTi2O5
Na
alpha Na3AlF6
beta Na3AlF6
NaAlO2
NaCl
NaCN
Na2CO3
NaF
NaH
NaO2
Na2O
Na2O2
NaOH
Na2S
Na2S2
Na2SiO3
Na2Si2O5
Na2SO4(I-V)
NH4Cl
P
monocl S
ortho S
alpha SiC
beta SiC
Si3N4
SiS2
alpha Ti
beta Ti
TiC
TiH2
TiN
alpha TiO
beta TiO
Ti2O3
Ti4O7
alpha Ti3O5
beta Ti3O5
a
Symbols for data are: B5 ⫽ Cp from Berman and Brown (1985), 298 K data from Berman (1983); B3 ⫽ Berman (1983); B8 ⫽ Berman (1988);
C ⫽ Hsieh et al. (1987); R ⫽ Robie et al. (1978); F ⫽ Fegley (1981); M ⫽ ‘MELTS’ software database (Ghiorso and Sack, 1995); J ⫽ Chase et
al. (1985) modified for consistency with Grønvold and Stølen (1992).
2.5. Thermodynamic Data and Models for Silicate Liquids
2.5.1. Test of MELTS: Peridotite KLB-1
A major innovation in the work presented here is the inclusion of the
“MELTS” model for silicate liquids (Ghiorso, 1985; Ghiorso and Sack,
1995), which describes the thermodynamic properties of silicate liquids
using a regular (symmetric) binary solution model in the components
SiO 2 –TiO 2 –Al 2 O 3 –Fe 2 O 3 –Fe 2 SiO 4 –Mg 2 SiO 4 –MgCr 2 O 4 –CaSiO 3 –
Na 2 SiO 3 –KAlSiO 4 –Ca 3 (PO 4 ) 2 –H 2 O, in addition to MnSi 0.5 O 2 –
NiSi0.5O2–CoSi0.5O2 which have been omitted in the present study.
Crystallization calculations with MELTS have been found to yield
remarkable agreement between calculated and observed amounts and
compositions of phases in liquid-crystal equilibrium experiments at 1
bar (Ghiorso and Carmichael, 1985) and at 10 kbar (Baker et al., 1995;
Hirschmann et al., 1998). Ghiorso and Sack (1995) caution against
using their model: (a) in systems containing only a small subset (⬍7)
of the components, or (b) far outside the temperature–pressure–
composition range of its calibration. Both of these caveats are addressed below.
Anticipating that condensate liquids will be poor in non-CMAS
components and will thus violate caveat (a), we tested MELTS calculations against quenched partial melting experiments of peridotite
KLB-1, whose non-CMAS components consist of only 8.1 wt.% FeO,
and ⱕ0.3% of all other oxides. Takahashi (1986) and Takahashi et al.
(1993) reported the temperature intervals between the observed absence and presence of phases, as well as phase compositions and melt
fractions for KLB-1 at 1 bar at the Ni–NiO oxygen buffer. Note that
only one of their seven data points used here is used in the MELTS
calibration database. It can be seen in Figure 1 that the MELTS model
reproduces the observed volume fractions of liquids well, except at low
melt fractions where there may be significant measurement error in the
experiments. The solidus temperature and appearance temperatures of
olivine, Ca–pyroxene, and feldspar agree nearly within experimental
error, but the model underpredicts the crystallization temperature of
orthopyroxene and overpredicts that of spinel (Table 5). Hirschmann et
344
D. S. Ebel and L. Grossman
Table 4. Solid solutions considered in the calculation, and sources of
solution models.
Metal alloy (this work)
Iron
Nickel
Silicon
Chromium
Cobalt
Fayalite
Forsterite
Monticellite
Fe
Ni
Si
Cr
Co
Olivine (Sack and Ghiorso, 1989; 1994b)
Fe2SiO4
Mg2SiO4
CaMgSiO4
2.5.2. Transition between liquid models
Melilite (Charlu et al., 1981)
Åkermanite
Gehlenite
Enstatite
Ferrosilite
Ca2MgSi2O7
Ca2Al2SiO7
Orthopyroxene (Sack and Ghiorso, 1989; 1994b)
Mg2Si2O6
Fe2Si2O6
Ca-pyroxene (Sack and Ghiorso, 1994a; 1994b; 1994c)
Diopside
CaMgSi2O6
Hedenbergite
CaFeSi2O6
Alumino-buffonite
CaTi0.5Mg0.5AlSiO6
Buffonite
CaTi0.5Mg0.5FeSiO6
Essenite
CaFeAlSiO6
Jadeite
NaAlSi2O6
Albite
Anorthite
Sanidine
used at lower temperatures where non-CMAS oxides are important
constituents of the liquid. The purely CMAS liquid region is very far
outside the composition range over which MELTS is calibrated, and
contains too few components for reliable application of the MELTS
liquid model. Furthermore, because the MELTS liquid uses mostly
silicate components, not pure oxides as end-members, it cannot be
applied to some especially Ca- and Al-rich regions of composition
space that are treated adequately by the CMAS liquid model. For
example, CaSiO3 is the major Ca-containing component employed by
MELTS; yet, early high temperature condensate liquids never contain
as much SiO2 as CaO. For these reasons, both models are required to
completely describe condensation of silicate liquids over the temperature ranges where liquids may be stable.
Feldspar (Elkins and Grove, 1990)
NaAlSi3O8
CaAl2Si2O8
KAlSi3O8
Chromite
Hercynite
Magnetite
Spinel
Ulvospinel
Spinel (Sack and Ghiorso, 1991a; 1991b)
FeCr2O4
FeAl2O4
Fe3O4
MgAl2O4
Fe2TiO4
Geikielite
Hematite
Ilmenite
Pyrophanite
Rhombohedral oxide (Ghiorso, 1990)
MgTiO3
Fe2O3
FeTiO3
MnTiO3
al. (1998) observed that the MELTS model overpredicted the crystallization temperature of orthopyroxene at 10 kbar. These differences
reflect compromises made by Sack and Ghiorso (1994c) to best satisfy
both high- and low-pressure pyroxene–liquid phase relations. In Figure
2, the 1 bar liquid compositions are compared with MELTS results,
with all Fe2O3 recalculated to FeO. The good agreement of the results
for melt fraction and composition suggests that the MELTS model will
yield reasonably accurate results in the condensation calculation, particularly because olivine dominates the distribution of mass in condensation sequences. Because spinel is a minor phase, overstabilization of
spinel will not have a significant effect on liquid stability. The understabilization of orthopyroxene, relative to liquid, suggests that liquid
stability might be slightly overpredicted when orthopyroxene condenses with it, and that the temperature of appearance of the latter
phase in the condensation calculation may be too low.
In addition to MELTS, Berman’s (1983) model for CMAS liquids is
included in the present work. Yoneda and Grossman (1995) used this
model, and explained in detail its advantages and drawbacks. The
CMAS liquid model works well at high temperatures, where these four
oxides are the only major ones condensed, but it is inadequate under
conditions where FeO, Na2O, and other non-CMAS components condense in appreciable quantities. Therefore, the MELTS model must be
A decision must be made as to when to switch from one model to the
other. In order to model non-CMAS oxides in the liquid, it would be
best to switch to the MELTS model at the highest feasible temperature.
For the case of 100⫻ dust enrichment at P tot ⫽ 10⫺3 bar, the curves in
Figure 3 illustrate the major oxide compositions of the two liquids,
calculated at 2 K intervals, near the appearance temperature of olivine,
indicated by the vertical line at 1782 K. The CMAS liquid is CaO- and
Al2O3-rich at high temperatures, but SiO2 and MgO increase rapidly
with decreasing temperature. By contrast, although a MELTS liquid
becomes stable well above 1782 K, it is CaO-deficient and SiO2enriched, relative to the CMAS liquid, because the only liquid the
MELTS model can determine to be stable must have sufficient SiO2 to
supply the required CaSiO3 component. That is, in the temperature
range above at least 1790 K, the most stable liquid possible in the
MELTS composition range is not the liquid which should be stable.
When the temperature of olivine appearance is reached, however, the
MELTS liquid has gained sufficient SiO2 and MgO to have a composition very similar to the CMAS liquid at the same temperature. Once
sufficient SiO2 has condensed, the MELTS model closely tracks the
Berman (1983) model liquid, but also accounts for increasing FeO and
TiO2 contents.
It was determined by performing condensation calculations with
each liquid separately that the CMAS liquid and the MELTS liquid
have nearly identical compositions at the temperature where olivine
becomes stable with CMAS liquid for 10⫺6 ⱕ P tot ⱕ 10⫺3, and 15⫻
ⱕ dust enrichment ⱕ 1000⫻. The criterion of olivine stability is,
therefore, used to trigger a switch from the CMAS liquid model to the
MELTS silicate liquid model in the calculations. The similarity in
oxide concentrations below the olivine stability temperature (Fig. 3)
could be expected from the similarity of the Berman (1983) database,
against which the CMAS model was calibrated, and the Berman (1988)
database, upon which the MELTS model relies. These comparisons
strongly suggest that the caveats cited by Ghiorso and Sack (1995)
regarding use of the MELTS liquid model are not egregiously violated
in its use below the condensation temperature of olivine.
3. RESULTS
3.1. Vapor of Solar Composition
Different thermodynamic data are employed for some crystalline phases, many more chemical species are included, and a
very different computational procedure was used in the present
study than in our previous work on condensation (Yoneda and
Grossman, 1995). It is therefore important to compare results
from the two studies, and this is done for the case of a solar gas
at P tot ⫽ 10⫺3 bar in Table 6. Appearance temperatures of
phases refer to the highest temperature step at which a phase is
part of the condensate assemblage in the 2 K steps of the
calculations. Our results are quite similar, but not identical, to
those of Yoneda and Grossman (1995), referred to as the
previous work in the following explanation of the differences
which, in all cases, are due to differences in thermodynamic
data. Note that, although some of the data used in our previous
Condensation in dust-enriched systems
345
Fig. 1. Comparison of melt fractions measured in peridotite melting experiments of Takahashi (1986) and Takahashi et
al. (1993) with those calculated at 1 bar using MELTS.
work may be more accurate, e.g., those for hibonite and grossite, we use those in Table 3 in the present study because the
latter are more consistent with the MELTS liquid model. Hibonite forms from corundum 15 K lower in the present calculations than in the previous work because hibonite is 2.5 kJ less
stable and corundum is 0.3 kJ more stable at 1700 K in the
present work. The lesser stability of hibonite in the present
work allows it to be replaced by grossite and CaAl2O4, which
are 16.7 and 8.7 kJ more stable, respectively, at 1700 K in the
present work. Here the gehlenite end-member of the melilite
solid solution series is 10.1 kJ less stable at 1600 K than it was
previously, and it forms from CaAl2O4, a phase more stable
than hibonite in the present calculations. This causes the appearance temperature of melilite to be suppressed by nearly 50
K and allows grossite and hibonite to partially replace it at
lower temperature. Spinel condenses 13 K lower in the present
work than it did previously, primarily because the MgAl2O4
end-member is now 3.5 kJ less stable at 1500 K. Plagioclase
forms from spinel ⬃10 K lower in the present work because the
CaAl2Si2O8 end-member is 6.5 kJ less stable at 1400 K than it
was previously. In the present work, Ti3O5 forms from Ti-
bearing clinopyroxene 18 K lower and Ti4O7 does not form at
all because of gross differences in the way the Ti-bearing
end-member components are treated in the two calculations. In
the previous work, literature data were used for the Ti3⫹-
Table 5. Comparison of experimental phase appearance temperatures
(Takahashi, 1986, run 4) with MELTS calculation for KLB-1, all at 1
bar.
Temperature (K)
Olivine in:
Spinel in:
Orthopyroxene in:
Ca-rich pyroxene in:
Feldspar in:
Liquid out:
Reported
Predicted by MELTS
⬎1973
1723–1773
1573–1623
1473–1523
1423–1448
1373–1423
1993
1838
1498
1473
1463
1368
Fig. 2. Comparison of measured compositions of KLB-1 liquids
(Takahashi, 1986; Takahashi et al., 1993) with those calculated from
MELTS, all at 1 bar. Asterisks indicate starting compositions in the
experiments.
346
D. S. Ebel and L. Grossman
Fig. 3. Compositions of CMAS and MELTS liquids near the olivine appearance temperature (vertical line at 1782 K) at
the stated conditions. In this temperature range, the MELTS liquid also contains ⬃1 wt.% of other oxides, which are not
shown.
bearing component CaTiAlSiO6 and estimated for the Ti4⫹bearing component CaTiAl2O6 while, in the present work, only
data for the Ti4⫹-bearing components CaTi0.5Mg0.5AlSiO6 and
CaTi0.5Mg0.5FeSiO6 are used. Cordierite replaces plagioclase
in the present work because it is 12.8 kJ/mol more stable, and
plagioclase is 7.2 kJ less stable, at 1300 K relative to the
previous work. Sphene does not form above 1200 K in the
present work because it is 5.5 kJ/mol less stable than it was
previously. No liquids were found to be stable in solar gas at
P tot ⫽ 10⫺3 bar by us or any previous workers, e.g., Wagner
(1979), Wood and Hashimoto (1993), and Yoneda and Grossman (1995), despite a contrary claim by Wark (1987).
3.2. General Effects of Dust Enrichment and Ptot
Complete condensation calculations were performed from
2400 K down to the last temperature step where our criteria for
adequate convergence could be met, usually between 1100 and
1300 K, and up to dust/gas enrichment factors of 1000⫻
relative to solar composition, hereinafter abbreviated as “dust
Table 6. Temperatures (K) of appearance and disappearance of condensates from a gas of solar composition at P tot ⫽ 10⫺3 bar, compared with
earlier results.
This work
Mineral
Yoneda and Grossman (1995)
In
Out
In
Out
Corundum
Hibonite
Grossite
Perovskite
CaAl2O4
Melilite ss.
Grossite
Hibonite
Spinel ss.
Metal ss.
Clinopyroxene ss.
Olivine ss.
Plagioclase ss.
Ti3O5
Orthopyroxene ss.
Ti4O7
Cordierite
Cr–spinel ss.
Sphene
1770
1728
1698
1680
1624
1580
1568
1502
1488
1462
1458
1444
1406
1368
1366
1726
1686
1594
1458
1568
1434
1502
1488
1400
1770
1743
1740
1500
1688
1448
1628
1444
1501
1464
1449
1443
1416
1386
1366
1361
1409
End of computation
1200
1330
1230
1318
1342
1221
1217
970
1361
1217
Condensation in dust-enriched systems
347
Table 7. Temperatures (K) of appearance and disappearance of condensates at P tot ⫽ 10⫺6 bar as a function of dust/gas enrichment.
Dust/gas enrichment:
Condensate
1⫻
100⫻
500⫻
1000⫻
In
Out
In
Out
In
Out
In
Out
Corundum
Hibonite
Perovskite
Grossite
CaAl2O4
Melilite
Grossite
Liquid
Melilite
Hibonite
Spinel
Liquid
Clinopyroxene
Olivine
Sapphirine
Metallic nickel–iron
Plagioclase
Cordierite
Orthopyroxene
Cr–spinel
Pyrophanite
MnO
1570
1480
1460
1440
1390
1370
1360
1470
1430
1270
1370
1360
1250
1300
1890
1790
1690
1760
1680
1630
1620
1790
1750
1500
1650
1620
1470
1550
2010
1940
1760
1910
1820
1760
1740
1740
1730
1930
1890
1610
1780
1740
1740
1670
1730
1630
2040
1980
1740
1960
1980
1950
1670
1820
1880
1370
1670
1630
1430
1610
1610
1390
1720
1660
End of computation
1100
1320
1270
1270
1210
1270
1240
1230
1210
1210
1200
1190
1160
1550
1540
1540
1430
1500
1490
1370
1660
1190
1190
1360
1440
1310
1400
1410
1130
1090
1300
1090
enrichments of 1000⫻”. The extremes of 10⫺3 and 10⫺6 bar
were chosen to bracket the generally accepted range of P tot in
the inner solar nebula (Wood and Morfill, 1988). Results are
shown at four different dust enrichments at 10⫺6 bar in Table
7 and at 10⫺3 bar in Table 8. In these tables, appearance and
disappearance temperatures are defined as the highest temperature steps at which a phase is either part of or becomes absent
from the stable condensate assemblage. In figures showing
1420
1450
1430
1410
1490
1610
1230
1180
1530
1660
1250
1210
1160
1200
1230
elemental distributions among coexisting phases, the fraction of
an element present in a phase at its appearance temperature is
extrapolated to zero in the next highest temperature step.
3.2.1. Oxygen fugacity
Shown in Figure 4 is the temperature dependence of the
oxygen fugacity of the gas in equilibrium with condensate
Table 8. Temperatures (K) of appearance and disappearance of condensates at P tot ⫽ 10⫺3 bar as a function of dust/gas enrichment.
Dust/gas enrichment:
Condensate
Liquid
Corundum
Hibonite
Grossite
Perovskite
CaAl2O4
Melilite
Grossite
Hibonite
Spinel
Metallic nickel–iron
Clinopyroxene
Olivine
Plagioclase
Orthopyroxene
␤-Ti3O5
Cordierite
Cr–spinel
Pyrophanite
MnO
Pyrrhotite
Whitlockite
End of computation
1⫻
100⫻
In
Out
1770
1720
1690
1680
1620
1580
1560
1500
1480
1460
1450
1440
1400
1360
1360
1330
1230
1720
1680
1590
1450
1560
1430
1500
1480
1400
1210
1310
500⫻
1000⫻
In
Out
In
Out
In
Out
2200
1390
⬎2400
1400
⬎2400
1310
1970
1810
1830
1690
1440
1780
1450
1620
1710
1990
1780
1420
1940
1430
1700
1940
2050
1800
1390
1990
1430
1990
1340
1600
1350
1300
1760
1400
1420
1330
1710
1380
1480
1380
1350
1200
1240
1260
348
D. S. Ebel and L. Grossman
Fig. 4. Variation of oxygen fugacity with temperature for gas in equilibrium with condensates at the stated conditions of
total pressure and dust enrichment, with the iron–wüstite buffer curve (dash-dot pattern) shown for reference.
assemblages computed at dust enrichments of 100⫻, 500⫻,
and 1000⫻ at P tot ⫽ 10⫺3 bar, and at dust enrichments of
100⫻ and 1000⫻ at 10⫺6 bar, along with that of the iron–
wüstite buffer (log f O2 ⫽ IW) and that of a gas of solar
composition at 10⫺3 bar (log f O2 ⬃ IW-6) for reference. The
curves for P tot ⫽ 10⫺3 bar are nearly concentric with one
another and show the expected increase of f O2 with increasing
dust enrichment. The curves for dust enrichments of 100⫻,
500⫻, and 1000⫻ lie at about IW-3.1, IW-1.7, and IW-1.2,
respectively. Exceptions to this concentric behavior are seen as
subtle changes in curvature, particularly noticeable at high dust
enrichments where the onset of olivine condensation removes
significant fractions of the oxygen from the vapor. Comparison
of the two curves for a constant dust enrichment of 100⫻
shows a slight increase in f O2 by as much as 0.4 log units as P tot
drops from 10⫺3 to 10⫺6 bar below 2000 K. The smallness of
the variation with P tot is due to the fact that f O2 in oxygen-rich
cosmic gases is largely controlled by the equilibrium H2 ⫹
1⁄2O ⫽ H O, and therefore depends on the P
2
2
H2O/P H2 ratio
which is almost independent of P tot at a given temperature, as
discussed by Yoneda and Grossman (1995). Above 2000 K,
however, Fig. 4 shows that, at dust enrichments of 100⫻ and
1000⫻, the f O2 values at 10⫺6 bar drop below their respective
values at 10⫺3 bar and the difference in f O2 between the two
total pressures at constant dust enrichment increases with increasing temperature, reaching nearly 4 log units at 2400 K.
This exceptionally large variation in f O2 with P tot is due to the
fact that, at 10⫺6 bar, almost all of the H2 and H2O are
dissociated into monatomic species at these high temperatures,
making the above equilibrium irrelevant to the f O2 while, at
10⫺3 bar, this dissociation occurs above 2400 K because the
higher pressure favors polyatomic over monatomic species.
3.2.2. Condensation temperatures and stability of liquid
The progressive increase in condensation temperatures of all
phases with increasing dust enrichment at constant P tot, as seen
by Yoneda and Grossman (1995), is illustrated in Tables 7 and
8. At 10⫺6 bar, condensation temperatures are still low enough
at a dust enrichment of 100⫻ that no liquid phase is stable.
However, at this P tot and above a dust enrichment between
400⫻ and 450⫻, the oxide ⫹ silicate fraction of the assemblage that condenses in certain temperature intervals, does so at
a temperature above the solidus temperature for its bulk chemical composition, causing liquid to be a stable condensate.
Upon cooling a system at 10⫺6 bar and a dust enrichment of
500⫻, liquid first appears at 1740 K, where melilite and
CaAl2O4 react with the gas to form grossite and a CMAS
liquid. This liquid field persists for only 10 K, at which point it
crystallizes into melilite and grossite. A liquid field reappears at
1630 K by reaction of melilite with the gas, and persists to 1390
K. At 10⫺6 bar and a dust enrichment of 1000⫻, condensation
of all phases occurs at even higher temperatures such that a
much greater range of bulk condensate compositions forms
above solidus temperatures, causing the liquid stability field to
extend to higher temperature, 1880 K, and to persist without
interruption to 1370 K, replacing the stability fields of
CaAl2O4, melilite, and grossite.
At constant dust enrichment, condensation temperatures of
all phases are higher at 10⫺3 bar than at 10⫺6 bar because
partial pressures of most condensable elements increase with
P tot. As a result, the minimum dust enrichment necessary to
condense partial melts at 10⫺3 bar is considerably lower than at
10⫺6 bar, and lies between 12⫻ and 13⫻. At 10⫺3 bar, there is,
at a dust enrichment of only 100⫻, an extensive and uninterrupted stability field of liquid extending up to 2200 K and
replacing the stability fields of corundum, hibonite, grossite,
CaAl2O4, and melilite. At higher dust enrichments at this P tot,
the liquid stability field extends to even higher temperatures.
One way of viewing trends in the size of the liquid stability
field as a function of P tot and dust enrichment is by comparison
of graphs of the distribution of silicon between condensed
phases and vapor vs. temperature. Such diagrams are presented
Condensation in dust-enriched systems
349
Fig. 5. Distribution of Si between condensed phases and gas at P tot ⫽ 10⫺6 bar and a dust enrichment of (a) 500⫻; and
(b) 1000⫻. Ca-px ⫽ Ca-rich clinopyroxene.
in Figs. 5a and 5b for 10⫺6 bar and dust enrichments of 500⫻
and 1000⫻, respectively, and should be compared to Figures
6d and 7d for the cases of 100⫻ and 1000⫻, respectively, at
10⫺3 bar. At 10⫺3 bar, the liquid has a stability field 800 K
wide (Table 8) and accounts for a maximum of 32% of the
silicon at a dust enrichment of 100⫻. At the same P tot, the
liquid field widens to ⬎1100 K, with a maximum of 60% of the
silicon, at a dust enrichment of 1000⫻. Although both the
temperature interval for the stability of liquid and the maximum
fraction of the total silicon accounted for by the liquid are
always smaller at 10⫺6 bar than at 10⫺3 bar for the same dust
enrichment, the liquid fields at 10⫺6 bar are still quite extensive
at these elevated dust enrichments. For example, although a
very small, high-temperature field of liquid is separated from a
lower-temperature liquid field at 500⫻, the latter field is 240 K
wide and accounts for a maximum of 25% of the silicon and, at
1000⫻, the liquid field is over 500 K wide and accounts for a
maximum of 26% of the silicon. Petaev and Wood (1998)
found no liquid stability field at 10⫺5 bar and a dust enrichment
of 107. This is in clear disagreement with the results of Wood
and Hashimoto (1993) who found a small liquid stability field
at the same P tot and a lower dust enrichment, 103, as both
studies employed the same liquid solution model and dust
composition. The Petaev and Wood (1998) results are also in
complete disagreement with ours in that we find a liquid
stability field at both lower P tot and lower dust enrichment.
Although the existence of a liquid stability field in Wood and
Hashimoto’s (1993) study is in general agreement with the
work presented here, both the amount of liquid and the temperature interval of its stability are much smaller than would be
expected from our work, presumably because of Wood and
Hashimoto’s (1993) use of an ideal solution model for silicate
liquids, which are demonstrably nonideal (Berman, 1983; Ghiorso et al., 1983), and the difference between their assumed
dust composition and ours.
From Tables 7 and 8, it is clear that the assemblage liquid ⫹
metallic nickel–iron ⫹ olivine ⫹ orthopyroxene ⫹ Cr–spinel
occupies a very wide stability field within the ranges of P tot and
dust enrichment considered herein.
3.3. Condensation at 100ⴛ Dust Enrichment and
Ptot ⴝ 10ⴚ3 Bar
The distributions of Al, Mg, Ca, Si, Fe, and Na and K
between condensed phases and vapor are illustrated in Figs. 6a,
6b, 6c, 6d, 6e, and 6f, respectively, for a system enriched 100⫻
in dust at P tot ⫽ 10⫺3 bar. The first condensate, a CMAS liquid
extremely rich in Al2O3 (79 mol%) and CaO (21%) with only
minor amounts of MgO and SiO2, condenses at 2200 K. Perovskite becomes stable at 1970 K, and consumes 85% of the
350
D. S. Ebel and L. Grossman
Fig. 6. Distribution of: (a) Al, (b) Mg, (c) Ca, (d) Si, (e) Fe, and (f) Na and K between condensed phases and vapor at
a dust enrichment of 100⫻ at P tot ⫽ 10⫺3 bar. Note vertical scale change in (e). Al–spinel ⫽ spinel with ⱕ1 wt.% Cr2O3;
Cr–spinel ⫽ spinel with ⬎1 wt.% Cr2O3. Other abbreviations as used previously.
total Ti in the system by 1850 K. At 1830 K, gaseous Mg, Fe,
and Cr begin to react with the liquid and perovskite to form an
Mg-, Al-rich spinel with minor amounts of Cr, Fe, and Ti. By
1810 K, this spinel has molar Fe/Mg and Cr/Al ratios of 3.4 ⫻
10⫺3 and 1.3 ⫻ 10⫺2, respectively, and a TiO2 content of 9.1
wt.%, so much Ti that perovskite disappears at this temperature. With falling temperature, Ti and Mg continue to condense
into spinel, and Si and Mg into the liquid. The SiO2 and MgO
contents of the liquid increase, and the MgAl2O4 component of
the spinel dissolves into the liquid. By 1780 K, the liquid
reaches ⬃40 wt.% SiO2 and ⬃26% MgO, olivine (0.25 wt.%
FeO, 0.73% CaO) becomes stable and, as discussed above, this
triggers the switchover from the CMAS to the MELTS liquid
model. At this point, the spinel has molar Fe/Mg and Cr/Al
ratios of 3.0 ⫻ 10⫺3 and 2.3 ⫻ 10⫺2, respectively and, because
Ti can now be accommodated by the liquid model, the TiO2
content of the liquid is 0.8 wt.% and Ti drops to only 0.44 wt.%
in the spinel. With falling temperature, most olivine forms by
wholesale condensation of Mg and Si from the gas but some by
crystallization of the liquid. With the total amount of liquid
decreasing slightly, the MgAl2O4 component of spinel continues to dissolve into it, causing the molar Fe/Mg and Cr/Al
Condensation in dust-enriched systems
351
Fig. 7. Distribution of: (a) Al, (b) Mg, (c) Ca, (d) Si, (e) Fe, and (f) Na and K between condensed phases and vapor at
a dust enrichment of 1000⫻ at P tot ⫽ 10⫺3 bar. Abbreviations as used previously.
ratios in spinel to rise to 9.0 ⫻ 10⫺3 and 6.2 ⫻ 10⫺2, respectively, just before spinel dissolves completely into the liquid at
1710 K. With falling temperature, the FeO content of olivine
increases and its CaO decreases, reaching 0.89 and 0.48%,
respectively, at the point where spinel disappears and 1.29%
and 0.42%, respectively, at 1690 K, the initial condensation
temperature of metallic NiFe. This alloy contains 13.6 wt.% Ni,
0.48% Co, and 0.24% Cr. As the temperature falls, olivine of
increasing FeO and decreasing CaO content continues to condense from the gas, Si and Fe continue to condense into the
liquid, diluting its MgO, Al2O3, and CaO contents, and metal of
decreasing Ni and Co and increasing Cr content continues to
condense. At 1620 K, when nearly all the Mg and 80% of the
Si are condensed, gaseous SiO begins to react with olivine and
liquid to form orthopyroxene, whose initial FeO content is 1.1
wt.%. At this point, olivine contains 1.9 wt.% FeO and 0.23%
CaO and the liquid contains 0.59 wt.% TiO2, 0.23% Cr2O3, and
0.30% FeO. At 1600 K, gaseous Cr begins to react with the
liquid to form a small amount of Cr–spinel, having molar
Fe/Mg and Cr/Al ratios of 0.049 and 2.1, respectively, and a
TiO2 content of 0.26 wt.%. With falling temperature, orthopyroxene of increasing FeO content continues to form by reaction
352
D. S. Ebel and L. Grossman
of gaseous SiO with liquid and with olivine of increasing FeO
and CaO contents; all components of the metal alloy continue
to condense, resulting in decreasing Ni, Co, and Cr contents;
the amount of Cr–spinel continues to increase at the expense of
Al2O3 in the liquid and gaseous Cr; and the CaO and TiO2
contents of the liquid increase while its FeO and Cr2O3 contents decrease. By 1550 K, 1.8% of the K has condensed into
the liquid which contains 0.01 wt.% K2O. At 1450 K, 99% of
the Fe is condensed, and gaseous Na begins to react with the
liquid to form plagioclase feldspar containing 1.6 mol% albite.
At this point, olivine contains 2.30 wt.% FeO and 0.34% CaO,
Cr–spinel has molar Fe/Mg and Cr/Al ratios of 0.053 and 1.43,
respectively, and 0.34 wt.% TiO2, and liquid contains 0.93
wt.% TiO2, 0.20% Cr2O3, 0.19% FeO, 0.06% K2O, and 0.01%
Na2O. At 1440 K, a diopsidic clinopyroxene begins to cocrystallize with feldspar from the remaining liquid, which reaches
0.15 wt.% K2O and 0.03% Na2O before disappearing at 1390
K. With continued cooling, gaseous Na and K react with
anorthitic feldspar, increasing its albite and orthoclase contents
and displacing Ca which, in turn, reacts with orthopyroxene to
form clinopyroxene and olivine. The FeO contents of olivine,
orthopyroxene, clinopyroxene, and spinel all increase as metallic Fe becomes oxidized, causing the Ni and Co contents of
the alloy to increase even as its Cr content decreases due to
reaction with spinel. At 1350 K, gaseous Mn reacts with Ti in
the spinel and clinopyroxene to form an oxide solid solution
consisting of pyrophanite [MnTiO3] with 9.4 wt.% MgO and
2.6% FeO. At 1300 K, the remaining gaseous Mn begins to
condense as MnO. By 1200 K, olivine contains 3.6 wt.% FeO
and 0.10% CaO; clinopyroxene contains 1.4% Al2O3, 0.62%
FeO, 0.25% TiO2, and 0.27% Na2O; spinel has molar Fe/Mg
and Cr/Al ratios of 0.13 and 5.1, respectively, and a TiO2
content of 0.59%; and the oxide solid solution contains only
1.3% MgO and 1.6% FeO. At this temperature, Na, K, and Mn
are only partially condensed, with 15%, 43%, and 3.5%, respectively, remaining in the vapor.
3.4. Condensation at 1000ⴛ and Ptot ⴝ 10ⴚ3 Bar
The distributions of Al, Mg, Ca, Si, Fe, and Na and K
between condensed phases and vapor are illustrated in Figs. 7a,
7b, 7c, 7d, 7e, and 7f, respectively, for a system enriched
1000⫻ in dust at P tot ⫽ 10⫺3 bar. At a dust enrichment of
1000⫻, a CMAS liquid is already present at 2400 K, into which
75% of the Al and 27% of the Ca have condensed. At 2050 K,
gaseous Ti, Mg, Cr, and Fe begin to react with Al2O3 in the
liquid to form a spinel containing 44.8 wt.% MgO, 39.5% TiO2,
12.7% Al2O3, 1.8% Cr2O3, 1.1% FeO, and 0.12% Fe2O3. At
1990 K, olivine begins to form primarily by condensation from
the gas but some also by crystallization from the liquid, and the
switch is made from the CMAS to the MELTS liquid model
which, because the latter can accommodate TiO2, causes the
titanian spinel to dissolve into the liquid. The initial olivine
contains 0.92 wt.% FeO and 0.23% CaO but, as Fe and Mg
condense into it, reaches 10.8% FeO and 0.13% CaO by 1800
K. Over the same temperature range, as Fe and Cr condense
into the liquid, the composition of the latter evolves from 0.73
wt.% FeO, 0.39% TiO2, 0.02% Cr2O3, and ⬍0.01% Fe2O3 to
24.2% FeO, 0.23% TiO2, 0.90% Cr2O3, and 0.19% Fe2O3.
Metal alloy containing 20.0 wt.% Ni, 0.70% Co, and 0.09% Cr
begins to condense at 1800 K, and reaches 11.7% Ni, 0.52%
Co, and 0.06% Cr by 1720 K. In this temperature range, olivine
continues to form at the expense of liquid and reaches 14.3
wt.% FeO and 0.13% CaO, while the liquid composition
evolves to 25.9 wt.% FeO, 0.25% TiO2, 1.22% Cr2O3, and
0.16% Fe2O3. At 1710 K, a small amount of Cr–spinel begins
to form by drawing Al and most of its Cr from the liquid but
some of its Cr also from the gas and the metal. Initially, it has
molar Fe/Mg and Cr/Al ratios of 0.62 and 3.79, respectively,
and contains 1.10 wt.% Fe2O3 and 0.27% TiO2, but varies in
composition as it continues to crystallize from the liquid with
falling temperature, reaching molar Fe/Mg and Cr/Al ratios of
1.34 and 2.29, respectively, with 1.42 wt.% Fe2O3 and 1.07%
TiO2 at 1440 K. Over the same temperature range, the amount
of olivine continues to increase with falling temperature, drawing its MgO, SiO2, and CaO from the liquid. From 1710 to
1560 K the FeO consumed by olivine comes from both liquid
and gas but, at 1560 K (the temperature below which ⬍1% of
the Fe remains in the gas) oxidation of the metal alloy joins the
liquid as a source of the FeO for continued production of
olivine. The amount of metal alloy increases with falling temperature from 1710 to 1560 K, as gaseous Fe continues to
condense into it, diluting its Ni, Co, and Cr concentrations to
9.3 wt.% Ni, 0.43% Co, and 0.01% Cr at 1560 K. Below 1560
K, however, oxidation of Fe causes the amount of metal to
decrease with falling temperature, increasing its Ni and Co
contents to 10.0 and 0.46 wt.%, respectively, by 1440 K. Its Cr
content continues to decrease due to formation of increasing
amounts of Cr–spinel with falling temperature. Olivine contains 21.1 wt.% FeO and 0.24% CaO at 1560 K, and 24.6%
FeO and 0.45% CaO at 1440 K. As the amount of liquid
decreases with falling temperature, its FeO, Cr2O3, and Fe2O3
contents progressively decrease, reaching 17.6 wt.%, 0.45%
and 0.02%, respectively, at 1560 K and 10.8%, 0.12%, and
0.01% at 1440 K; and its TiO2, Na2O, K2O, and P2O5 contents
progressively increase, reaching 0.43 wt.%, 0.29%, 0.10%, and
⬍0.01%, respectively, at 1560 K and 0.56%, 2.79%, 0.35%,
and 0.20% at 1440 K. At 1480 K, MnO condenses and, at 1430
K, plagioclase containing 34.4 mol% albite and 0.35% orthoclase begins to crystallize from the liquid. As the amount of
plagioclase increases with falling temperature, its albite and
orthoclase contents also increase. Although the Na required for
this is supplied by both gas and liquid, the K is derived only
from the liquid, with the proportion of K residing in the vapor
actually increasing initially with falling temperature. At 1390
K, a diopside-rich clinopyroxene, containing 4.7 wt.% FeO,
2.3% Al2O3, 0.18% Na2O, 0.36% TiO2, and 0.09% Fe2O3,
crystallizes from the liquid. At 1380 K, a pyrophanite-rich
oxide solid solution, containing 9.53 wt.% FeO, 1.02% MgO,
and 0.52% Fe2O3, forms by reaction of gaseous Mn with TiO2
in the liquid; and gaseous sulfur begins to react with metallic Fe
to form pyrrhotite, Fe0.877S. The concentrations of Ni and Co in
the residual alloy are 11.5 wt.% and 0.53%, respectively, but
increase sharply as more pyrrhotite forms with falling temperature, reaching 21.4% and 0.98%, respectively, at 1310 K. At
1350 K, gaseous P reacts with the liquid to form whitlockite. At
1320 K, just before disappearing, the liquid contains 10.1 wt.%
Na2O, 4.52% FeO, 1.34% K2O, 0.77% P2O5, 0.41% TiO2 and
0.02% Cr2O3. At 1260 K, olivine contains 27.3 wt.% FeO and
0.31% CaO; clinopyroxene contains 4.5 wt.% FeO, 1.6%
Condensation in dust-enriched systems
353
Fig. 8. Mole fraction of iron end-member at 10⫺3 bar in: (a) olivine and (b) orthopyroxene and at 10⫺6 bar in (c) olivine
and (d) orthopyroxene as a function of temperature and at dust enrichment factors with integral multiples of 100.
Trajectories of the condensation temperature of metallic nickel–iron alloy, the temperature at which direct condensation of
olivine ceases, the temperature at which ⬎98% of the total iron is condensed, and the temperature of disappearance of
silicate liquid are indicated.
Al2O3, 0.33% Na2O, 0.33% TiO2, and 0.07% Fe2O3; Cr–spinel
has molar Fe/Mg and Cr/Al ratios of 2.9 and 7.5, respectively,
and contains 2.8 wt.% TiO2 and 1.5% Fe2O3; the pyrophaniterich solid solution contains 9.2 wt.% FeO, 0.86% MgO, and
0.45% Fe2O3; and the metal alloy contains 27.5 wt.% Ni and
1.3% Co. At this point, 97.8% of the P is condensed as
whitlockite, 65.1% of the sulfur as pyrrhotite, and 90.0% of the
Na and 65.5% of the K as feldspar. The ratio of the proportion
of Fe in sulfide to that in metal is 2.2.
3.5. Direct Condensation of Oxidized Iron at High
Temperature
The historical motivation behind studying dust enrichment in
the solar nebula was to increase the oxygen fugacity so as to
produce condensates that are more oxidized than is possible in
a gas of solar composition. For example, one of the most
perplexing problems for condensation theory is how to produce
the observed molar Fe/Fe ⫹ Mg ratios that range from 0.2 in
olivine and pyroxene in H-group ordinary chondrites, to 0.3 in
the LL group, to 0.5 or above in the matrices of some CV3
chondrites. Solar gas is so reducing that all Fe condenses
initially as metal. In order to produce FeO-rich silicates, oxidation of this metal, which occurs only at or below ⬃500 K,
must be followed by diffusion of Fe2⫹ through the crystal
structures of pre-existing silicates. This requires equilibration
between solids and a low-density gas and efficient diffusion
through nearly close-packed silicate structures at temperatures
where the rates of these processes are so low that most workers
doubt chondritic matter obtained its oxidation state in this way.
The extent to which this problem is alleviated here is illustrated by the fayalite content of olivine and ferrosilite content
of orthopyroxene, which are plotted as functions of temperature
at various dust enrichments at 10⫺3 bar in Figs. 8a and b and at
10⫺6 bar in Figs. 8c and 8d. In the dust-enriched systems
considered in these calculations, the oxygen fugacity is so high
that significant amounts of FeO are stable in olivine and pyroxene at very high temperatures, where gas–solid equilibration
is much more likely and diffusion rates are expected to be much
higher than at the low temperatures where FeO would become
stable in a solar gas. In dust-enriched systems, not only does the
first-condensing olivine contain significant quantities of FeO,
but also, as the temperature falls below the initial condensation
temperature of olivine, the equilibrium fayalite content is predicted to increase while additional olivine condenses from the
gas. In this temperature interval of direct olivine condensation,
Fe2⫹ is incorporated into each olivine grain as it grows directly
354
D. S. Ebel and L. Grossman
from the vapor phase. The assumption of thermodynamic equilibrium requires that all olivine at a given temperature have the
same fayalite content, and that is the value computed here. This
requires that the relatively fayalite-poor olivine condensed at
high temperature must become as fayalite-rich as newly condensing olivine at a lower temperature. If, even at the high
temperatures being discussed here, the Fe2⫹ contents of the
interiors of the previously formed olivine crystals cannot increase fast enough to maintain equilibrium, the newly condensing olivine at any temperature will have even higher fayalite
contents than calculated here. For all dust enrichments considered here at 10⫺6 bar, and for dust enrichments ⬍800⫻ at 10⫺3
bar, we can consider this stage, olivine formation by direct
condensation from the gas, to end at the temperature where
olivine begins to react with the gas to form orthopyroxene. For
dust enrichments ⱖ800⫻ at 10⫺3 bar, however, direct condensation of olivine ceases at a higher temperature than that for
orthopyroxene formation because the fraction of the total Si
remaining in the gas becomes very small, ⬍1%. The trajectory
of the temperature of cessation of direct olivine condensation is
marked on Figs. 8a and 8c. At both values of P tot, a liquid is
present which persists to temperatures well below that where
orthopyroxene begins forming. The FeO contents of olivine and
orthopyroxene continue to rise with falling temperature and,
with liquid present, this can occur by equilibration of olivine
and orthopyroxene with the liquid. This is a much more kinetically favorable process for forming FeO-rich silicates than
equilibration with a low-density gas.
At 10⫺3 bar, X Fa for the first-condensing olivine is only
2.5 ⫻ 10⫺3, 5.1 ⫻ 10⫺3, and 9.1 ⫻ 10⫺3 at dust enrichments
of 100⫻, 500⫻, and 1000⫻, respectively. At the temperature
where olivine condensation ends, however, X Fa has increased
to 0.019, 0.088, and 0.164 at dust enrichments of 100⫻, 500⫻,
and 1000⫻, respectively, and, at the temperature of disappearance of liquid, X Fa is 0.025, 0.14, and 0.31. At 10⫺6 bar, X Fa is
lower in the first-condensing and last-condensing olivine than
at 10⫺3 bar and the same dust enrichment, and almost the same
at the temperature where the liquid disappears. Below the
solidus, continued increase in the FeO content of olivine with
decreasing temperature is governed by multiphase equilibrium,
which would be impeded not only by slow diffusion of Fe2⫹
into silicates but also by slow solid-state reaction rates between
olivine, orthopyroxene, clinopyroxene, and plagioclase, and by
slow reaction between gaseous oxidizing agents and metallic
iron. If the arbitrary assumption is made that multiphase equilibrium can be maintained to temperatures as low as 1200 K,
nebular olivine can be expected to have X Fa of 0.036 and 0.21
at dust enrichments of 100⫻ and 500⫻, respectively, at 10⫺3
bar, and 0.036, 0.23, and 0.40 at dust enrichments of 100⫻,
500⫻, and 1000⫻, respectively, at 10⫺6 bar. Higher FeO
contents require equilibration to lower temperatures under
these conditions or condensation at higher dust enrichments.
At a given P tot, the temperature at which gaseous SiO begins
to react with olivine to form orthopyroxene increases, reaches
a maximum, and finally decreases with progressively increasing dust enrichment. At a dust enrichment of 1000⫻, there is no
orthopyroxene stability field at all at 10⫺3 bar. At relatively low
dust enrichments, the orthopyroxene condensation temperature
increases with increasing dust enrichment due to the attendant
increase in the partial pressure of SiO. Accompanying this,
Fig. 9. Concentrations of: (a) major and (b) minor components of the
total condensate as a function of temperature at the stated conditions.
Filled circles indicate average composition of H-group chondrites.
however, is an increase in the (FeO ⫹ MgO)/SiO2 ratio of the
silicate fraction of the condensate due to the increase in oxygen
fugacity with increasing dust enrichment. This tends to stabilize
olivine at the expense of orthopyroxene. A dust/gas ratio is
reached beyond which the stabilizing effect on orthopyroxene
of the increasing partial pressure of SiO is outweighed by the
stabilizing effect on olivine of the increasing (FeO ⫹ MgO)/
SiO2 ratio. This causes the orthopyroxene field to shrink at the
expense of the olivine field with increasing dust/gas ratio, and
eventually disappear altogether.
3.6. Bulk Chemical Composition of Condensates
In Figures 9a and 9b, the bulk chemical composition of the
total condensate is plotted as a function of temperature at a P tot
of 10⫺3 bar and a dust enrichment of 560⫻. Features of this
diagram which are common to condensation at all dust enrichments are the early entry of Al, Ca, and Ti relative to Mg and
Si, as well as the relatively late entry of Na, K, and Mn into the
condensates. Features specific to condensation at this dust
enrichment are the relative proportions of metal, FeO, and
sulfide as a function of temperature. This particular dust enrichment was chosen because it yields a single temperature at
which the distribution of Fe between metal, sulfide, and silicate
matches closely the distribution found in H-group ordinary
chondrites and results in a bulk chemical composition very
close to the average of those meteorites. For example, at 1310
K the total condensate and, for comparison (brackets), the
average H-group chondrite fall from Jarosewich (1990) contain
18.8 (17.8) wt.% Fe ⫹ Ni ⫹ Co metal, 10.2 (10.3)% FeO, 5.9
(5.4)% FeS, 34.2 (36.6)% SiO2, and 24.6 (23.3)% MgO. Similarly, at the same P tot and a slightly higher dust enrichment of
Condensation in dust-enriched systems
355
Fig. 10. Compositions of condensate liquids at: (a), (b) 10⫺3 bar and a dust enrichment of 100⫻; (c), (d) 10⫺3 bar and
a dust enrichment of 1000⫻; and (e), (f) 10⫺6 bar and a dust enrichment of 1000⫻. In all cases, the vertical line marks the
condensation temperature of olivine, where the transition between CMAS and MELTS liquid models is made. In (e) and
(f), Na2O ⱕ 0.01 wt.%. Inflection points are due to the onset of crystallization or disappearance of a coexisting phase, and
are labelled as follows: a, spinel in; d, metal in; e, orthopyroxene in; f, Cr–spinel in; g, feldspar in; h, clinopyroxene in; k,
rhombohedral oxide in; p, perovskite in; q, clinopyroxene in and liquid out.
675⫻, a temperature can be found at which the bulk chemical
composition of the condensate comes very close to the average
composition of L-group chondrite falls from Jarosewich
(1990). In the following comparison, sufficient metal of the
same composition as that in Jarosewich’s average L-group
chondrite has been added to his average L-group chondrite bulk
composition to yield the same atomic Fe/Si ratio as in H-group
chondrites. At 1330 K, the condensate contains 16.8 (16.1)
wt.% metal, 12.9 (13.2)% FeO, 5.5 (5.3)% FeS, 34.0 (36.3)%
SiO2, and 24.5 (22.6)% MgO. In both cases, the MgO/SiO2
ratio of the condensate is higher than in the chondrite due to the
fact that the relative abundances of nonvolatile elements in the
model system are those of Cl chondrites, which are known to
have a higher atomic Mg/Si ratio than ordinary chondrites.
Nevertheless, the close correspondence in composition between
the predicted condensates and the chondrite averages serves to
emphasize the point that the distribution of iron between metal,
silicate, and sulfide in ordinary chondrites could have been
established during high-temperature condensation in a dustenriched system.
3.7. Composition of Silicate Liquid
The temperature variation of the composition of the silicate
melt is shown for the cases of 10⫺3 bar and a dust enrichment
of 100⫻ in Figures 10a and 10b, 10⫺3 bar and a dust enrichment of 1000⫻ in Figures 10c and 10d, and for 10⫺6 bar and
a dust enrichment of 1000⫻ in Figures 10e and 10f. The
evolution of the liquid composition is similar in all cases, but
some exceptions are noteworthy. Because Al is more refractory
than Ca, the Al2O3 content of the initial liquid is very high but
falls with decreasing temperature due to dilution by CaO which
condenses more gradually with falling temperature. Similarly,
at lower temperatures, incipient condensation of more volatile
356
D. S. Ebel and L. Grossman
Fig. 10 (Continued)
Si and Mg into the liquid causes the concentrations of SiO2 and
MgO to increase, diluting both Al2O3 and CaO. Comparing
Figs. 10a and 10c it is seen that for liquids that form at higher
temperatures than olivine, similar liquid compositions are stable at temperatures 300 K higher when the dust enrichment is
increased by a factor of 10 at 10⫺3 bar. Similarly, comparing
Figs. 10c and 10e reveals that liquids of similar composition
form about 400 K higher when P tot is increased by a factor of
1000 at a dust enrichment of 1000⫻. Note however that at the
condensation temperatures of olivine, liquid compositions are
quite different from one another at different combinations of
P tot and dust enrichment. For example, the concentrations of
MgO and SiO2 in the liquid at a dust enrichment of 1000⫻ are
almost the same where olivine condenses at 10⫺3 bar (Fig. 10c)
but the SiO2 content is more than double that of MgO at 10⫺6
bar (Fig. 10e). One way of understanding this is by considering
the fact that the solubility of olivine in a melt of a given
composition is quite different at temperatures hundreds of
degrees apart.
Below the condensation temperature of olivine, the main
difference in major element trends of the liquid at different
combinations of P tot and dust enrichment, aside from those of
FeO and alkalis, is the failure of the SiO2 concentration to level
off with falling temperature at a dust enrichment of 1000⫻ at
10⫺3 bar (Fig. 10c) as it does at a dust enrichment of 100⫻ at
10⫺3 bar (Fig. 10a) and 1000⫻ at 10⫺6 bar (Fig. 10e). This is
entirely due to the absence of orthopyroxene from the crystalline assemblage in equilibrium with the liquid at a dust enrichment of 1000⫻ at 10⫺3 bar. It is the condensation of this phase
that triggers the flattening of the SiO2 curve under the other sets
of conditions. Of the three cases shown, it is at a dust enrichment of 1000⫻ and 10⫺3 bar where the Cr2O3 content of the
liquid is highest, climbing to 1.2 wt.% with falling temperature,
and then declining after Cr–spinel becomes stable at 1710 K
(Fig. 10d). At a dust enrichment of 100⫻ at 10⫺3 bar, this
phase becomes stable at 1600 K, before the Cr2O3 content of
the liquid reaches 0.36 wt.% (Fig. 10b). At a dust enrichment of
1000⫻ at 10⫺6 bar, Cr–spinel coexists with the MELTS liquid
over its entire stability range, preventing its Cr2O3 content from
exceeding 0.28 wt.% (Fig. 10f). As the amount of liquid becomes vanishingly small during near-solidus crystallization of
clinopyroxene and plagioclase, concentrations of TiO2 are seen
to build up in the last dregs of liquid. Only at a dust enrichment
of 1000⫻ at 10⫺3 bar does this trend reverse itself. This is due
Condensation in dust-enriched systems
357
Fig. 10. (Continued)
to stabilization of a pyrophanite-rich solid solution at a temperature above that for the disappearance of liquid. As seen by
comparing Figs. 10b, 10d, and 10f, alkali contents of the liquid
increase both with increasing P tot and with increasing dust
enrichment because the partial pressures of sodium and potassium increase with both parameters. As a result, Na2O and K2O
concentrations in the liquid are negligible at 10⫺6 bar, even at
a dust enrichment of 1000⫻. In the other cases shown, Na2O
and K2O concentrations rise above negligible levels only
within 100 to 200 K of the temperature of disappearance of
liquid, reaching maxima of 10.1 and 1.3 wt.%, respectively, at
10⫺3 bar and a dust enrichment of 1000⫻. At a dust enrichment
of 1000⫻, the FeO content of the liquid at 10⫺3 bar is higher
than at 10⫺6 bar at most temperatures (Figs. 10c and 10e),
considerably so at some temperatures. Because f O2 is only
weakly dependent on P tot at 1500 to 1600 K, the higher FeO
content of the liquid is due simply to the higher P Fe at higher
P tot, which causes a greater proportion of the iron to be condensed at any given temperature.
In most cases, the liquid disappears in the temperature interval 1370 to 1400 K, the approximate location of the peridotite
solidus at 1 bar (see Table 5). An exception to this general rule
is found in Table 8 for the case of a dust enrichment of 1000⫻
at 10⫺3 bar, where the liquid persists to 1310 K. At the same
P tot and a dust enrichment of 500⫻, the liquid disappears at a
significantly higher temperature, 1400 K. Similarly, at the same
dust enrichment (1000⫻) and lower P tot (10⫺6 bar) the liquid
also disappears at a much higher temperature (1370 K). At
10⫺3 bar, the reason for the different solidification temperatures at the different dust enrichments is evident from a comparison of the liquid compositions in the two cases at 1410 K,
the last temperature step before the liquid disappears at a dust
enrichment of 500⫻. At this temperature, the liquid at the
lower dust enrichment contains slightly less Na2O (2.67 wt.%)
and much less FeO (3.26%) than the liquid at the higher dust
enrichment (3.81% and 9.46%, respectively) and high concentrations of both of these oxides are known to depress solidus
temperatures. At a dust enrichment of 1000⫻, the reason for
the different solidification temperatures at the different total
pressures is found in the different liquid compositions at 1380
K, the last temperature step before the liquid disappears at 10⫺6
bar. Although the FeO content of the liquid is slightly lower at
10⫺3 than at 10⫺6 bar, 7.54 vs. 9.51 wt.%, the Na2O concentration is much higher at 10⫺3 than at 10⫺6 bar, 5.89 vs. ⬍0.01
358
D. S. Ebel and L. Grossman
existence, may be artifacts of the inability of the CMAS liquid
to accommodate Ti. The incoming of the MELTS liquid causes
the very Ti-rich spinel at 1000⫻ and 10⫺3 bar to dissolve
suddenly, and the less Ti-rich spinel at 100⫻ and 10⫺3 bar to
dissolve gradually before disappearing. The even lower Ti
spinel at 1000⫻ and 10⫺6 bar continues to crystallize with
falling temperature, gradually becoming first more Cr-rich and
then more Fe-rich. As shown in Fig. 11c, the Cr/Al ratio levels
off below 1390 K, as formation of spinel continues by reaction
of gaseous Cr with Al2O3 in the liquid. When spinel re-forms
in the two cases at 10⫺3 bar, its Cr/Al ratio falls, as the spinel
draws down Al2O3 from the liquid while deriving its Cr from
the metal alloy and the gas at 100⫻, and from the metal alloy
and the liquid at 1000⫻. In all three cases, these trends are
interrupted by plagioclase formation, which draws Al2O3 from
the MgAl2O4 component of the spinel, increasing the Cr/Al
ratio and decreasing the amount of spinel. Plagioclase formation also causes an increase in the rate of increase of the
number of Ti cations in the spinel with decreasing temperature,
accompanied by an increase in the number of Mg and/or Fe
ions in accordance with the above coupled substitution. At
lower temperature, the number of Ti ions in the spinel begins to
decrease with decreasing temperature due to extraction of Ti
into pyrophanite or, at 100⫻ and 10⫺3 bar, clinopyroxene.
3.9. Composition of Clinopyroxene
Fig. 11. Composition of spinel as a function of temperature at: (a)
P tot ⫽ 10⫺3 bar and a dust enrichment of 100⫻; (b) P tot ⫽ 10⫺3 bar
and a dust enrichment of 1000⫻; and (c) P tot ⫽ 10⫺6 bar and a dust
enrichment of 1000⫻. Inflection points labelled as in Fig. 10, plus: b,
perovskite out; c, olivine in; j, liquid out; m, MnO in; n, pyrrhotite in;
r, orthopyroxene out.
wt.%. This is because the partial pressure of Na is more than a
factor of 200 higher at 1380 K at 10⫺3 bar than at 10⫺6 bar.
Furthermore, because Na continues to condense into the liquid
in this temperature range, the lower the temperature to which
the liquid persists, the higher its Na2O content becomes, and
this further lowers the ultimate temperature of its disappearance.
3.8. Composition of Spinel
The numbers of cations in spinel per four oxygen atoms are
plotted as a function of temperature at dust enrichments of
100⫻ and 1000⫻ at 10⫺3 bar in Figures 11a and 11b, respectively, and 1000⫻ at 10⫺6 bar in Figure 11c. In all cases, the
highest temperature spinel forms by reaction of gaseous Mg
with TiO2 in perovskite and Al2O3 in the CMAS liquid, except
at 1000⫻ and 10⫺3 bar, where all Ti is from the gas. In this
spinel, the Ti cations first increase with falling temperature as
perovskite and/or gaseous Ti are consumed and then decrease
sharply when the MELTS liquid, which can accommodate Ti,
becomes stable. Both stages proceed in accordance with the
coupled substitution of Mg2⫹ ⫹ Ti4⫹ ⫽ 2Al3⫹, and are accompanied by steadily rising numbers of Fe and Cr cations
which are condensing from the gas. As discussed previously,
the high Ti contents of these spinels and possibly even their
The concentrations of FeO, Al2O3, and TiO2 in clinopyroxene are plotted as a function of temperature at 10⫺3 bar and
dust enrichments of 100⫻ and 1000⫻, and at 10⫺6 bar and
1000⫻ in Figures 12a, 12b, and 12c, respectively. The amount
of clinopyroxene increases with falling temperature in all three
cases due either to crystallization from the liquid or, after liquid
is exhausted, to reactions among plagioclase, orthopyroxene,
and olivine, as can be seen in Figs. 6 and 7 for the cases at 10⫺3
bar. The proportion of the total Fe accounted for by clinopyroxene increases with falling temperature as metal is oxidized,
but the concentration of FeO may rise or fall depending on the
relative rates of formation of Mg and Fe end-members. Similarly, the proportions of the total Al and Ti accounted for by
clinopyroxene increase with falling temperature as this phase
crystallizes from the liquid in the cases at 10⫺3 bar, but the
concentrations of Al2O3 and TiO2 may increase or decrease
with falling temperature due to the relative formation rates of
the different pyroxene end-members. At 10⫺3 bar and 100⫻
and at 10⫺6 bar and 1000⫻, a temperature is reached below
which the Al2O3 and TiO2 concentrations begin to fall with
decreasing temperature, as plagioclase begins to draw its
Al2O3, and pyrophanite its TiO2, from clinopyroxene.
3.10. Composition of Feldspar
The mole fractions of albite and orthoclase in feldspar are
plotted as functions of temperature at 10⫺3 bar and dust enrichments of 100⫻ and 1000⫻ in Figure 13. The amount of
feldspar and its albite and orthoclase contents increase steadily
with decreasing temperature in both cases. Above the temperature of disappearance of liquid, feldspar draws its Na from
both liquid and gas, but its K from the liquid only. Below this
temperature, Na and K continue to condense from the gas into
Condensation in dust-enriched systems
Fig. 12. Composition of Ca-rich clinopyroxene as a function of
temperature at: (a) P tot ⫽ 10⫺3 bar and a dust enrichment of 100⫻; (b)
P tot ⫽ 10⫺3 bar and a dust enrichment of 1000⫻; and (c) P tot ⫽ 10⫺6
bar and a dust enrichment of 1000⫻. Inflection points as previously
labelled.
feldspar, increasing their concentrations in feldspar with decreasing temperature. At 10⫺6 bar and dust enrichments of
100⫻ and 1000⫻, K contents of feldspar are vanishingly small
down to the last temperature step of the computations shown in
Table 7. This is also true for Na at 100⫻, but X Ab at 1000⫻
rises to 0.1 at 1200 K.
Fig. 13. Mole fractions of albite (Ab) and orthoclase (Or) in feldspar
as a function of temperature at P tot ⫽ 10⫺3 bar and a dust enrichment
of 100⫻ and 1000⫻. Inflection points as previously labelled.
359
Fig. 14. Mole % of: (a) Ni; (b) Co; and (c) Cr in metallic nickel–iron
alloy as a function of temperature at the stated conditions. Inflection
points as previously labelled.
3.11. Composition of Metallic Nickel–Iron
The concentrations of Ni, Co, and Cr in the metallic nickel–
iron alloy at various combinations of P tot and dust enrichment
are shown in Figs. 14a, 14b, and 14c, respectively. Under all
conditions shown, Ni and Co are slightly more refractory and
have slightly steeper condensation curves than Fe. This leads to
high concentrations of Ni and Co in the first-condensing alloys,
steadily declining concentrations of Ni and Co with falling
temperature as condensation of slightly less refractory Fe dilutes the previously condensed Ni and Co, and finally a leveling
off of the Ni and Co contents when all three elements are totally
condensed. At still lower temperatures in the more oxidizing
cases, 1000⫻ at 10⫺3 and 10⫺6 bar, Ni and Co contents begin
to rise very gradually with falling temperature due to oxidation
of the Fe component of the alloy. At 1380 K at 1000⫻ and
10⫺3 bar, the Ni and Co contents of the alloy begin to rise very
sharply with falling temperature due to reaction of gaseous
sulfur with the Fe component of the alloy to form pyrrhotite.
Under oxidizing conditions, Cr is slightly more refractory than
Fe and, like Ni and Co, falls steadily in concentration with
falling temperature. Under more reducing conditions, however,
the behavior of Cr is completely different. At 100⫻ and 10⫺3
bar, Cr is slightly less refractory than Fe, its concentration in
the metal increases sharply with falling temperature in the
high-temperature alloys, and only reverses itself below the
formation temperature of Cr–spinel, which extracts Cr from the
metal alloy. The increase in Cr content with falling temperature
is not seen at 100⫻ and 10⫺6 bar because most of the Cr has
360
D. S. Ebel and L. Grossman
Fig. 15. Bulk chemical compositions of metallic nickel–iron ⫹
pyrrhotite condensate assemblages predicted at P tot ⫽ 10⫺3 bar and the
stated dust enrichments, projected onto the liquid-crystal phase relations of the Fe-rich portion of the Fe–S binary system. Dashed curves
show projections of phase boundaries when 7 mol % Ni is present.
already condensed as Cr–spinel at a higher temperature than
that where the metal alloy begins to condense. While high Si
concentrations in metallic nickel–iron alloys can result from
condensation from gases more reducing than a gas of solar
composition, X Si is always ⬍10⫺4 in the systems considered in
this work.
1262 K and well within the field of ␥–iron ⫹ Fe–S liquid. The
solid assemblage of metallic nickel–iron ⫹ pyrrhotite predicted
by our thermodynamic model to condense under these conditions is thus seen to form at temperatures where it is actually
metastable relative to metallic iron ⫹ Fe–S liquid. Nickel,
cobalt, and chromium are also predicted to condense into the
metal alloy, but the amounts of Co and Cr are quite small and
the phase relations are seen to change very little with the
addition of 7% Ni, a fairly representative concentration in these
condensate assemblages. We conclude that, at these relatively
high total pressures and dust enrichments, direct condensation
of iron–sulfide liquids will occur. Furthermore, because the
liquid-bearing assemblage obviously has a lower Gibbs free
energy than the predicted assemblage, the temperature of appearance of sulfide liquid will actually be higher than the
condensation temperature of pyrrhotite. Recall that the silicate
liquid in the 500⫻ case solidifies at 1400 K, which is well
above the minimum condensation temperature of sulfide liquid,
but that the silicate liquid at 1000⫻ does not solidify until 1310
K, almost 100 K below the minimum condensation temperature
of sulfide liquid in this case. This means that, at the highest dust
enrichment factors at high P tot, condensation of coexisting
silicate and sulfide liquids occurs, assuming they are not miscible.
4. DISCUSSION
4.1. Stability of Silicate Liquid in Solar Gas
3.12. Metal–Sulfide Condensate Assemblages
Because of the high concentration of sulfur in dust of Cl
composition, enrichment in such dust leads to much higher f S2
and permits sulfide phases to condense at higher temperatures
at a given P tot than in a gas of solar composition. Inspection of
Table 7 reveals that no sulfide phase becomes stable above the
last temperature step of the calculations at any of the dust
enrichments shown at 10⫺6 bar, but that at 10⫺3 bar pyrrhotite
(Fe0.877S) joins metallic nickel–iron as a stable condensate at
1330 and 1380 K at dust enrichments of 500⫻ and 1000⫻,
respectively. These temperatures are higher than minimum
melting temperatures in the Ni-poor part of the Fe–Ni–S system
but, since our computer program does not contain a thermodynamic model for Fe–Ni–S liquids, it would be unable to predict
their existence even if they were more stable than the metal ⫹
pyrrhotite assemblages that are predicted. In order to see if
sulfide liquids are more stable than the predicted assemblages,
the relative atom proportions of Fe and S were calculated for
the metallic nickel–iron ⫹ pyrrhotite assemblage predicted at
each temperature step for dust enrichments of 500⫻, 800⫻,
and 1000⫻ at 10⫺3 bar, and are plotted on a portion of the
liquid-crystal phase relations in the Fe–S binary (Chuang et al.,
1986a) in Figure 15. The dashed curves in this figure are the
phase boundaries that result from addition of 7% Ni to the
system, taken from the work of Hsieh et al. (1982), projected
onto the Fe–S plane. Under all conditions, the trajectory of the
condensate compositions initially falls vertically along the left
margin of the diagram until the temperature of pyrrhotite formation is reached. Below this, the trajectories extend to the
right and downward, well above the eutectic temperature of
The calculations show that no liquids are stable in a gas of
solar composition, even at a total pressure as high as 10⫺3 bar.
Any liquids formed by the partial or complete melting of
agglomerated solids (Whipple, 1966; Lofgren, 1996) would
therefore be highly unstable with respect to partial evaporation
in a solar nebula of canonical composition, and would become
even more unstable with decreasing pressure. Such liquids
would lose FeO and alkali metals most readily, followed by Mg
and Si, then Ca and Al with increasing temperature.
Experimentally determined evaporation rates of Na2O from
liquids of chondrule composition (Radomsky and Hewins,
1990; Tsuchiyama et al., 1981; Yu and Hewins, 1998) show
that Na loss is faster at lower total pressures and lower f O2.
However, Lewis et al. (1993) showed that sodium loss in alkali
olivine basalt melt droplets (3.05 wt.% Na2O) was nearly
attenuated upon heating above 1600 K at P tot ⫽ 1 bar, at the
iron–wüstite buffer in a CO/CO2 ⫹ NaCl vapor with P Na ⬎
4 ⫻ 10⫺6 atm. The present calculations show that these conditions are roughly equivalent to a Cl dust enrichment factor
well in excess of 1000⫻ at 10⫺3 bar. Lewis et al. (1993), based
on their experiments and following Wood (1984), suggested
chondrule formation in ‘clumps’ where the local partial pressures of condensable elements and oxygen were enhanced by
volatilization of chondrule precursor material. The phase diagrams presented above provide the rigorous thermochemical
basis for concluding that such a mechanism would indeed
stabilize liquids in the solar nebula and reduce or eliminate the
driving force for volatilization of Na and other elements from
chondrule-like liquids.
Condensation in dust-enriched systems
361
Fig. 16. Bulk compositions of chondrules, and bulk compositions of condensed oxides at 10⫺3 bar. Data: filled squares ⫽
type IA (Jones and Scott, 1989); filled diamonds ⫽ type IB (Jones, 1994); filled circles ⫽ type IAB (Jones, 1994); filled
triangles ⫽ type IIA (Jones, 1990); open squares ⫽ type IIB (Jones, 1996); open circles ⫽ H3 (Lux et al., 1981); open
triangles ⫽ CM and CO (Rubin and Wasson, 1986); open diamonds ⫽ Manych L3 (Dodd, 1978). Circles on each path
correspond to compositions at 1800, 1700, 1600, 1500, 1400, and 1300 K with increasing FeO ⫹ Na2O. Dashed extensions
of paths are subsolidus compositions to 1200 K for 100⫻ and 300⫻ and to 1250 K for 800⫻. Star represents the bulk
composition of peridotite KLB-1 (Takahashi, 1986).
4.2. Chondrules in Dust-enriched Systems
Is there some pressure and dust enrichment at which the
temperature variation of the bulk composition of the condensed
matter, exclusive of metal, resembles the composition range of
chondrules? For example, are chondrules the quenched droplets
of the solid ⫹ liquid assemblages that formed by equilibrium
condensation at various temperatures? In Figure 16, chondrule
compositions spanning the common composition range are
plotted in the forsterite-rich corner of the ternary (CaO ⫹
Al2O3)–(MgO ⫹ SiO2)–(FeO ⫹ Na2O ⫹ K2O). This perspective is useful because the apices correspond to groups of oxides
which condense in distinct temperature ranges, and these seven
oxides constitute the bulk of chondritic material. Superposed on
these chondrule compositions are paths representative of the
trajectories of bulk oxide condensates, exclusive of metal, with
decreasing temperature. Each of the condensation paths sweeps
down from the CaO ⫹ Al2O3 apex toward the field occupied by
type IA chondrules (Jones and Scott, 1989), close to the
MgO ⫹ SiO2 corner. Note that no single path for a particular
combination of P tot and dust enrichment will be able to account
for all of the chondrule compositions plotted. Of the cases
shown, only the one at the highest dust enrichment, 800⫻, is
oxidizing enough to make sufficient FeO at high temperature
that the condensation trajectory passes through the field of type
IIA (Jones, 1990) chondrules at temperatures above that where
dust and gas could be expected to equilibrate, i.e., ⬃1200 K.
This case is so oxidizing, however, that significant FeO condenses before complete condensation of MgO and SiO2, causing the trajectory to peel away from the (CaO ⫹ Al2O3)–
(MgO ⫹ SiO2) join before reaching the MgO ⫹ SiO2 corner
and thus only to graze the top of the field of type IA chondrules.
The condensation paths at lower dust enrichments (100⫻ and
300⫻) are seen to penetrate the type IA field only slightly
more, missing the vast majority of the data points in it as well
as the type IIA field. Similar composition trajectories to these
are obtained at P tot ⬍ 10⫺3 bar but, at a given dust enrichment,
the temperatures at which the trajectories reach high FeO ⫹
alkali contents become progressively lower with decreasing
P tot. Sequestration of high-temperature, Ca-, Al-rich condensates could cause the condensation path of the remaining system at a particular P tot and dust enrichment to pass through the
middle of the field of type IA chondrules, but such a path would
then graze only the bottom of the field of type IIA chondrules.
An example of such a path is shown in Fig. 16 for the case of
condensation of a system having a dust enrichment of 800⫻ but
from which 72% of the Al2O3 and CaO have been removed.
Given the wide range of CaO ⫹ Al2O3 contents of the chondrules in Fig. 16, it is conceivable that a family of condensation
curves corresponding to a single P tot and a high dust enrichment but variable amounts of sequestration of high-temperature
condensates could account for the observed data. Although
such an appeal to a multitude of adjustable parameters appears
to satisfy the data, the separate roles of FeO and alkalies are not
addressed in Figure 16.
The FeO and Na2O contents of the same chondrules shown
in Figure 16 are illustrated in Figure 17. Representative oxide
bulk compositions for condensation paths at 100⫻, 300⫻,
500⫻, and 800⫻ dust enrichment (the latter with and without
362
D. S. Ebel and L. Grossman
Fig. 17. Sodium and iron oxide contents of the chondrules of Fig. 16 and of KLB-1, with representative paths of bulk
oxide condensates. Compositions reported as ⱕ0.03% Na2O are plotted at 0.03%.
removal of 72% of the Al2O3 and CaO) at 10⫺3 bar are
superposed on Fig. 17, with the subsolidus portions dashed.
The FeO contents of the calculated condensate assemblages at
high dust enrichments reach the levels found in chondrules at
high temperatures, but Na2O contents only approach the levels
found in Na-rich chondrules near the solidus of silicate liquid.
The compositions of the chondrules richest in both Na2O and
FeO, which include the type IIA and IIB chondrules of Jones
(1990; 1996) and many of those reported by Dodd (1978), are
more Na2O-rich than compositions on any of the equilibrium
condensation paths calculated under the conditions investigated
here. This result precludes formation of these particular chondrules by representative sampling of equilibrium condensate
assemblages from dust-enriched systems at specific temperatures, either by quenching and isolating primary condensates or
by isochemical melting and quenching of such samples at
P tot ⱕ 10⫺3 bar and dust enrichments ⱕ1000⫻. Dust enrichment factors of ⬎800⫻ are not required, however, to produce
the iron contents observed in most chondrules. If the FeO
contents of chondrules did result from the formation and isolation of their precursors in a dust-enriched environment, their
Na contents may have resulted from some secondary, as yet
unspecified process.
Evidence for only limited intracrystal and liquid-crystal
equilibrium in chondrules includes the presence of grains interpreted to be relict olivine and/or pyroxene (Steele, 1986) and
chemical zoning in phenocrysts of porphyritic chondrules (Simon and Haggerty, 1979; Jones and Scott, 1989). Because
diffusion of major elements in silicate liquids is generally much
faster than through crystals, the liquid is likely to have been the
last phase to have even partially equilibrated with ambient
vapor, and the glass is thus the most likely phase to have
preserved a record of the temperature, pressure, and composition of the vapor. In fact, radial chemical zonation in mesostasis
of unequilibrated chondrules, particularly with respect to Na2O
(Ikeda and Kimura, 1985; DeHart et al., 1988; Grossman et al.,
1997) suggests that some chondrules underwent only partial
equilibration at a late stage in their formation, possibly with
surrounding gas. Are there conditions for which the liquids in
equilibrium with dust-enriched vapor have the same compositions as the glass found in chondrules? Plotted in Figure 18 are
the compositions of the mesostasis from most of the chondrules
whose bulk compositions are illustrated in the previous two
figures. The axes of Fig. 18 are the same as those of Figure 16,
and the composition trajectories for the liquid fraction of the
condensates at two dust enrichments are superposed on Figure
18, starting at the temperature where olivine first condenses,
and the transition from CMAS to MELTS liquid models occurs.
The calculated liquids move away from forsterite toward the
CaO ⫹ Al2O3 apex, then begin to become enriched in iron.
Once past the peak in iron content, the paths differ in trajectory,
due to differences in the proportions of crystallizing olivine and
orthopyroxene, and liquid. Continuing olivine and pyroxene
crystallization drives the liquid trajectory steeply away from
the MgO ⫹ SiO2 corner, causing CaO and Al2O3 concentrations to rise in the liquid until feldspar and pyroxene crystallize,
very near the solidus, driving CaO and Al2O3 downward again.
The liquid paths in Figure 18 suggest that chondrule glasses
with high FeO ⫹ alkali oxide contents could have equilibrated
with a highly dust-enriched gas at 10⫺3 bar. The glass compositions observed in type IA chondrules, however, contain much
less MgO ⫹ SiO2 than any FeO- or alkali-bearing liquids in
equilibrium with dust-enriched vapor. In these particular chondrules, it is mostly Na2O content which pulls the liquid composition off the CMAS join, into the interior of the triangle.
This can be seen in Figure 19, which shows glass compositions
of the same chondrules, with paths of liquid composition for
four dust enrichment factors superposed. Type IA chondrules
fall closest to the y-axis. In the case of 1000⫻ enrichment at
10⫺3 bar, the FeO contents of calculated liquids increase to
Condensation in dust-enriched systems
363
Fig. 18. Glass compositions in chondrules, with paths of condensate liquids for 500 and 800⫻ Cl dust enrichment, from
below the appearance temperatures of olivine to their solidi. Symbols for chondrule data as in Fig. 16. Grey circles on each
path mark 100° decrements starting at 1700 K.
⬎25 wt.% while Na2O ⬍ 0.1 wt.%, then decrease with decreasing temperature. Past the peak in FeO content, Na begins
to condense into liquids, and Na2O concentrations increase
steeply near the solidus, at which points the curves in Fig. 19
terminate. Prior to Na condensation, P Na is ⬃2.7 ⫻ 10⫺6 bar at
a dust enrichment of 1000⫻, almost three times higher than that
at 300⫻. Because of this and the slightly higher f O2 in the most
dust-enriched systems (800⫻ and 1000⫻) a significant fraction
of the Na condenses into the liquid above 1400 K. As a result,
below 1400 K, Na2O contents of the calculated liquids at dust
enrichments of 800⫻ and 1000⫻ are in the range of those of
many of the chondrules shown, and the calculated P Na is very
similar for all dust enrichments, varying from ⬃3.2 ⫻ 10⫺7 bar
at a dust enrichment of 800⫻ to ⬃4.8 ⫻ 10⫺7 bar at 1000⫻ at
Fig. 19. Glass compositions in chondrules, with paths of condensate liquids for 300, 500, 800, and 1000⫻ Cl dust
enrichment, which terminate at their solidi. Data as in Fig. 18.
364
D. S. Ebel and L. Grossman
1350 K. The most important reason why the Na2O contents of
the liquids at the highest dust enrichments reach the levels
found in chondrules, while those at the lowest dust enrichments
(300⫻ and 500⫻) do not is the persistence of the former to
lower solidus temperatures, ⬃1300 K vs. ⬃1400 K (Fig. 8). As
discussed above, this is due to higher FeO and Na2O contents
of the liquids in the more dust-enriched systems at 1400 K. At
constant dust enrichment, our calculations show that maximum
alkali contents of the liquids decrease substantially with decreasing P tot. Even at P tot as high as 10⫺4 bar and a dust
enrichment of 1000⫻, for example, the maximum Na2O content of the liquid is at least a factor of 5 smaller than at 10⫺3 bar
and the same dust enrichment. Except for the type I chondrule
glasses with Na2O/FeO wt. ratios ⬎ 2.0, and type II chondrule
glasses with very high FeO and Na2O contents, all the chondrule glass compositions examined here could represent silicate
liquids in equilibrium with dust-enriched vapor within 200° of
their solidus temperatures at P tot ⬎ 10⫺4 bar. Even if the
precursors of the most FeO- and Na2O-rich chondrules were
melted in a gas enriched 1000⫻ by dust, their liquids would
have lost sodium by evaporation or FeO by reduction, assuming
that they were hot for a long enough time to have equilibrated
with the gas.
5. CONCLUSIONS
Condensation of systems sufficiently enriched in dust of Cl
composition to yield ferromagnesian silicates with molar FeO/
(FeO ⫹ MgO) ratios of 0.1 to 0.4 at temperatures above 1200
K also produces copious molten silicate. The distribution of Fe
between metal, silicate, and sulfide in specific classes of ordinary chondrites can be produced by high-temperature condensation at specific dust enrichments. While a rigorous thermodynamic model at last shows how direct condensation of
silicate liquid can occur within the range of P tot thought to have
existed in the inner part of the solar nebula, the compositions of
the partially molten condensates so formed do not match the
compositions of types I and II chondrules in important ways.
Such chondrules are thus secondary objects that did not form
by direct condensation. Nevertheless, if chondritic matter owes
its oxidation state to condensation of dust-enriched systems, the
present work shows the sequence of condensation, details of the
condensation reactions, and the evolution of the compositions
of solid and liquid solution phases that may be relevant to the
formation of chondrites and the precursors to chondrules. The
present work also gives physico-chemical conditions capable of
stabilizing against evaporation silicate liquids of specific compositions, some of which are similar to the compositions of
some chondrule glasses, in cosmic gases at low nebular pressures.
Acknowledgments—The authors extend thanks to J. Valdes, S. Champion, D. Archer, and G. Miller for technical assistance, and to M. S.
Ghiorso and R. O. Sack for providing advice and the MELTS code.
Critical reviews by J. R. Beckett and an anonymous reviewer were very
helpful. Material support for this project was through NASA grants
NAGW-3340 and NAG5-4476.
REFERENCES
Anders E. and Grevesse N. (1989) Abundances of the elements: Meteoritic and solar. Geochim. Cosmochim. Acta 53, 197–214.
Anderson G. M. and Crerar D. (1993) Thermodynamics in Geochemistry. Oxford U. Press.
Baker M. B., Hirschmann M. M., Ghiorso M. S., and Stolper E. M.
(1995) Compositions of near-solidus peridotite melts from experiments and thermodynamic calculations. Nature 375, 308 –311.
Barin I. (1989) Thermochemical data of pure substances. VCH.
Berman R. G. (1983) A thermodynamic model for multicomponent
melts, with application to the system CaO–MgO–Al2O3–SiO2.
Ph.D., Univ. British Columbia.
Berman R. G. (1988) Internally-consistent thermodynamic data for
minerals in the system Na2O–K2O–CaO–MgO–FeO–Fe2O3–Al2O3–
SiO2–TiO2–H2O–CO2. J. Petrol. 29, 445–522.
Berman R. G. and Brown T. H. (1985) Heat capacity of minerals in the
system
Na2O–K2O–CaO–MgO–FeO–Fe2O3–Al2O3–SiO2–TiO2–
H2O–CO2. Contrib. Mineral. Petrol. 89, 168 –183.
Betts J. T. (1980) A compact algorithm for computing the stationary
point of a quadratic function subject to linear constraints. ACM
(Association for Computing Machinery) Trans. Mathematical Software 6, 391–397.
Charlu T. V., Newton R. C., and Kleppa O. J. (1981) Thermochemistry
of synthetic Ca2Al2SiO7 (gehlenite)–Ca2MgSi2O7 (åkermanite) melilites. Geochim. Cosmochim. Acta 45, 1609 –1617.
Chase M. W., Jr., Davies C. A., Downey J. R., Frurip D. J., McDonald
R. A., and Syverud A. N. (1985) JANAF Thermochemical Tables,
3rd ed. J. Phys. Chem. Ref. Data 14, Suppl. 1.
Chuang Y.-Y., Hsieh K.-C., and Chang Y. A. (1986a) Thermodynamics and phase relationships of transition metal-sulfur systems: Part V.
A reevaluation of the Fe–S system using an associated solution
model for the liquid phase. Metall. Trans. 16B, 277–285.
Chuang Y.-Y., Hsieh K.-C., and Chang Y. A. (1986b) A thermodynamic analysis of the phase equilibria of the Fe–Ni system above
1200 K. Metall. Trans. 17A, 1373–1380.
Connolly H. C., Jr. and Burnett D. S. (1999) Minor element distributions in spinels from Type B CAI: An experimental study. Lunar
Planet. Sci. XXX, Abstract #1459 (CD-ROM).
DeHart J. M., Sears D. W. G., and Lofgren G. E. (1988) Sodium
enriched luminescent chondrule mesostasis rims in the unequilibrated ordinary chondrites. Meteoritics 23, 265 (abstr.).
Dodd R. T. (1978) The composition and origin of large microporphyritic chondrules in the Manych (L-3) chondrite. Earth Planet. Sci.
Lett. 39, 52– 66.
Ebel D. S. and Grossman L. (1996) Limiting conditions for silicate
liquid stability in cosmic gases. Meteoritics Planet. Sci. Suppl. 31,
A40 –A41 (abstr.).
Ebel D. S. and Grossman L. (1997a) Direct condensation of ferromagnesian liquids from cosmic gases. Lunar Planet. Sci. XXVIII, 317–
318 (abstr.).
Ebel D. S. and Grossman L. (1997b) Stability of alkali and iron oxides
in condensate liquids. Meteoritics Planet. Sci. Suppl. 32, A37 (abstr.).
Ebel D. S. and Grossman L. (1998) Effect of dust enrichment on solid
and liquid compositions in equilibrium with cosmic gases. Lunar
Planet. Sci. XXIX, Abstract #1421 (CD-ROM).
Ebel D. S., Ghiorso M. S., Sack R. O., and Grossman L. (1999) Gibbs
energy minimization in gas ⫹ liquid ⫹ solid systems. Submitted to
J. Computational Chem.
Elkins L. T. and Grove T. L. (1990) Ternary feldspar experiments and
thermodynamic models. Am. Mineral. 75, 544 –559.
Fegley B. J., Jr. (1981) The thermodynamic properties of silicon
oxynitride. J. Am. Ceram. Soc. 64, C-124 –C-126.
Fegley B. J., Jr. and Palme H. (1985) Evidence for oxidizing conditions
in the solar nebula from Mo and W depletions in refractory inclusions in carbonaceous chondrites. Earth Planet. Sci. Lett. 72, 311–
326.
Ghiorso M. S. (1985) Chemical mass transfer in magmatic processes I.
Thermodynamic relations and numerical algorithms. Contrib. Mineral. Petrol. 90, 107–120.
Ghiorso M. S. (1990) Thermodynamic properties of hematite–ilmenite– geikielite solid solutions. Contrib. Mineral. Petrol. 104, 645–
667.
Ghiorso M. S. (1994) Algorithms for the estimation of phase stability
in heterogeneous thermodynamic systems. Geochim. Cosmochim.
Acta 58, 5489 –5501.
Condensation in dust-enriched systems
Ghiorso M. S. and Carmichael I. S. E. (1985) Chemical mass transfer
in magmatic processes II. Applications in equilibrium crystallization,
fractionation and assimilation. Contrib. Mineral. Petrol. 90, 121–
141.
Ghiorso M. S. and Sack R. O. (1995) Chemical mass transfer in
magmatic processes IV. A revised and internally consistent thermodynamic model for the interpolation and extrapolation of liquid–
solid equilibria in magmatic systems at elevated temperatures and
pressures. Contrib. Mineral. Petrol. 119, 197–212.
Ghiorso M. S., Carmichael I. S. E., Rivers M. L., and Sack R. O. (1983)
The Gibbs free energy of mixing of natural silicate liquids; an
expanded regular solution approximation for the calculation of magmatic intensive variables. Contrib. Mineral. Petrol. 84, 107–145.
Grønvold F. and Stølen S. (1992) Thermodynamics of iron sulfides II.
Heat capacity and thermodynamic properties of FeS and of Fe0.875S
at temperatures from 298.15 K to 1000 K, of Fe0.98S from 298.15 K
to 800 K, and of Fe0.89S from 298.15 K to about 650 K. Thermodynamics of formation. J. Chem. Thermodyn. 24, 913–936.
Grossman J. N., Alexander C. M. O’D., and Wang J. (1997) Zoning of
trace elements and deuterium in the mesostasis of low-FeO chondrules in Semarkona. Lunar Planet. Sci. XXVIII, 481– 482 (abstr.).
Grossman L. (1972) Condensation in the primitive solar nebula.
Geochim. Cosmochim. Acta 36, 597– 619.
Hirschmann M. (1991) Thermodynamics of multicomponent olivines
and the solution properties of (Ni, Mg, Fe)2SiO4 and (Ca, Mg,
Fe)2SiO4 olivines. Am. Mineral. 76, 1232–1248.
Hirschmann M. M., Ghiorso M. S., Wasylenki L. E., Asimow P. D.,
and Stolper E. M. (1998) Calculation of peridotite partial melting
from thermodynamic models of minerals and melts I: Methods and
comparison with experiments. J. Petrol. 39, 1091–1115.
Hsieh K.-C., Chang Y. A., and Zhong T. (1982) The Fe–Ni–S system
above 700°C (iron–nickel–sulfur). Bull. Alloy Phase Diagrams 3,
165–172.
Hsieh K.-C., Vlach K. C., and Chang Y. A. (1987) The Fe–Ni–S
system I. A thermodynamic analysis of the phase equilibria and
calculation of the phase diagram from 1173 to 1623 K. High Temp.
Sci. 23, 17–37.
Ikeda Y. and Kimura M. (1985) Na–Ca zoning of chondrules in
Allende and ALHA-77003 carbonaceous chondrites. Meteoritics 20,
670 – 671 (abstr.).
Jarosewich E. (1990) Chemical analyses of meteorites: A compilation
of stony and iron meteorite analyses. Meteoritics 25, 323–337.
Jones R. H. (1990) Petrology and mineralogy of type II, FeO-rich
chondrules in Semarkona LL3.0: Origin by closed-system fractional
crystallization, with evidence for supercooling. Geochim. Cosmochim. Acta 54, 1795–1802.
Jones R. H. (1994) Petrology of FeO-poor, porphyritic pyroxene chondrules in the Semarkona chondrite. Geochim. Cosmochim. Acta 58,
5325–5340.
Jones R. H. (1996) FeO-rich, porphyritic pyroxene chondrules in unequilibrated chondrites. Geochim. Cosmochim. Acta 16, 3115–3138.
Jones R. H. and Scott E. R. D. (1989) Petrology and thermal history of
type IA chondrules in the Semarkona (LL3.0) chondrite. Proc. 19th
Lunar Planet. Sci. Conf., 523–536.
Knacke O., Kubaschewski O., and Hesselmann K. (1991) Thermochemical Properties of Inorganic Substances. Springer-Verlag.
Lattimer J. M., Schramm D. N., and Grossman L. (1978) Condensation
in supernova ejecta and isotopic anomalies in meteorites. Astrophys.
J. 219, 230 –249.
Lewis R. D., Lofgren G. E., Franzen H. F., and Windom K. E. (1993)
The effect of Na vapors on the Na content of chondrules. Meteoritics
28, 622– 628.
Lofgren G. E. (1996) A dynamic crystallization model for chondrule
melting. In Chondrules and the Protoplanetary Disk (eds. R. H.
Hewins et al.), pp. 187–196. Cambridge U. Press.
Lux G., Keil K., and Taylor G. J. (1981) Chondrules in H3 chondrites:
Textures, compositions and origins. Geochim. Cosmochim. Acta 45,
675– 685.
Normanton A. S., Moore R. H., and Argent B. B. (1976) A calorimetric
and mass-spectrometric study of solid iron– chromium alloys. Metal
Sci. 10, 207–213.
Palme H. and Fegley B. J., Jr. (1990) High-temperature condensation of
365
iron-rich olivine in the solar nebula. Earth Planet. Sci. Lett. 101,
180 –195.
Pedley J. B. and Marshall E. M. (1983) Thermochemical data for
gaseous monoxides. J. Phys. Chem. Ref. Data 12, 967–981.
Petaev M. I. and Wood J. A. (1998) Mineral equilibrium in fractionated
nebular systems. II. A new code embracing 18 elements. Lunar
Planet. Sci. XXIX, Abstract #1474 (CD-ROM).
Radomsky P. M. and Hewins R. H. (1990) Formation conditions of
pyroxene– olivine and magnesian olivine chondrules. Geochim. Cosmochim. Acta 54, 3475–3490.
Robie R. A., Hemingway B. S., and Fisher J. R. (1978) Thermodynamic properties of minerals and related substances at 298.15 K and
1 bar (105 Pascals) pressure and at higher temperatures. USGS Bull.
1452.
Rubin A. and Wasson J. T. (1986) Chondrules in the Murray CM2
meteorite and compositional differences between CM–CO and ordinary chondrite chondrules. Geochim. Cosmochim. Acta 50, 307–315.
Rubin A., Fegley B. J., Jr., and Brett R. (1988) Oxidation state in
chondrites. In Meteorites and the Early Solar System (eds. J. F.
Kerridge and M. S. Matthews), pp. 488 –511. U. Arizona Press.
Sack R. O. and Ghiorso M. S. (1989) Importance of considerations of
mixing properties in establishing an internally consistent thermodynamic database: Thermochemistry of minerals in the system
Mg2SiO4–Fe2SiO4–SiO2. Contrib. Mineral. Petrol. 102, 41– 68.
Sack R. O. and Ghiorso M. S. (1991a) An internally consistent model
for the thermodynamic properties of Fe–Mg–titanomagnetite–aluminate spinels. Contrib. Mineral. Petrol. 106, 474 –505.
Sack R. O. and Ghiorso M. S. (1991b) Chromian spinels as petrogenetic indicators: Thermodynamic and petrological applications. Am.
Mineral. 76, 827– 847.
Sack R. O. and Ghiorso M. S. (1994a) Thermodynamics of multicomponent pyroxenes: I. Formulation of a general model. Contrib. Mineral. Petrol. 116, 277–286.
Sack R. O. and Ghiorso M. S. (1994b) Thermodynamics of multicomponent pyroxenes: II. Phase relations in the quadrilateral. Contrib.
Mineral. Petrol. 116, 287–300.
Sack R. O. and Ghiorso M. S. (1994c) Thermodynamics of multicomponent pyroxenes: III. Calibration of Fe2⫹(Mg)⫺1, TiAl2(MgSi2)⫺1,
TiFe3⫹2(MgSi2)⫺1, AlFe3⫹(MgSi)⫺1, NaAl(CaMg)⫺1, Al2(MgSi)⫺1
and Ca(Mg)⫺1 exchange reactions between pyroxenes and silicate
melts. Contrib. Mineral. Petrol. 118, 271–296.
Sakao H. and Elliott J. F. (1975) Thermodynamics of dilute bcc Fe–Si
alloys. Metal. Trans. 6A, 1849 –1851.
Sharp C. M. and Wasserburg G. J. (1995) Molecular equilibria and
condensation temperatures in carbon-rich gases. Geochim. Cosmochim. Acta 59, 1633–1652.
Simon S. B. and Haggerty S. E. (1979) Petrography and olivine mineral
chemistry of chondrules and inclusions in the Allende meteorite.
Proc. 10th Lunar Planet. Sci. Conf., 871– 883.
Smith W. R. and Missen R. W. (1982) Chemical Reaction Equilibrium
Analysis: Theory and Algorithms. Wiley.
Sorby H. C. (1877) On the structure and origin of meteorites. Nature
15, 495– 498.
Steele I. M. (1986) Compositions and textures of relic forsterite in
carbonaceous and unequilibrated ordinary chondrites. Geochim.
Cosmochim. Acta 50, 1379 –1395.
Stull D. R. and Prophet H. (1970) JANAF Thermochemical Tables, 2nd
ed. U.S. National Bureau of Standards.
Takahashi E. (1986) Melting of a dry peridotite KLB-1 up to 14 GPa:
Implications on the origin of peridotitic upper mantle. J. Geophys.
Res. 91, 9367–9382.
Takahashi E., Shimazaki T., Tsuzaki Y., and Yoshida H. (1993) Melting study of a peridotite KLB-1 to 6.5 GPa, and the origin of basaltic
magmas. Philos. Trans. R. Soc. London A 342, 105–120.
Tsuchiyama A., Nagahara H., and Kushiro I. (1981) Volatilization of
sodium from silicate melt spheres and its application to the formation
of chondrules. Geochim. Cosmochim. Acta 45, 1357–1367.
Van Schmus W. R. (1969) The mineralogy and petrology of chondritic
meteorites. Earth-Science Rev. 5, 145–184.
Wagner R. D. (1979) The condensation and stability of chemically
heterogeneous systems, M.S. thesis. Arizona State University.
Wark D. A. (1987) Plagioclase-rich inclusions in carbonaceous chon-
366
D. S. Ebel and L. Grossman
drite meteorites: Liquid condensates? Geochim. Cosmochim. Acta
51, 221–242.
Weinbruch S., Palme H., Müller W. F., and El Goresy A. (1990) FeO-rich
rims and veins in Allende forsterite: Evidence for high temperature
condensation at oxidizing conditions. Meteoritics 25, 115–125.
Whipple F. L. (1966) Chondrules: Suggestion concerning the origin.
Science 153, 54 –56.
Wood J. A. (1967) Olivine and pyroxene compositions in type II
carbonaceous chondrites. Geochim. Cosmochim. Acta 31, 2095–2108.
Wood J. A. (1984) On the formation of meteoritic chondrules by
aerodynamic drag heating in the solar nebula. Earth Planet. Sci. Lett.
70, 11–26.
Wood J. A. and Hashimoto A. (1993) Mineral equilibrium in fractionated nebular systems. Geochim. Cosmochim. Acta 57, 2377–
2388.
Wood J. A. and Morfill G. E. (1988) Solar nebula models. In Meteorites
and the Early Solar System (eds. J. F. Kerridge and M. S. Matthews),
pp. 329 –347. Univ. Arizona Press.
Yoneda S. and Grossman L. (1995) Condensation of CaO–MgO–
Al2O3–SiO2 liquids from cosmic gases. Geochim. Cosmochim. Acta
59, 3413–3444.
Yu Y. and Hewins R. (1998) Transient heating and chondrule formation: Evidence from sodium loss in flash heating simulation experiments. Geochim. Cosmochim. Acta 62, 159 –172.